# Whether Economic Freedom Is Significantly Related to Death of COVID-19

Authors: Ray-Ming Chen
Journal: Journal of Healthcare Engineering
 (2020)

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## Abstract

COVID-19 has caused a huge mayhem globally. Different economic freedom leads to different performances of a country’s reaction to the pandemic. We study 164 countries and apply mathematical and statistical approaches to tackle the problem: whether economic freedom has a significant impact on the death of COVID-19. We devise a metric, some norms, and some orderings to construct an absolute reference and the actual relation via binary sequences. Then, we use the theoretical binary sequences to construct a probability distribution which linearises the strength of relation between economic freedom and death of COVID-19. Then, the actual relation from the data analysis provides an evidence to the hypothetical testing. Our analysis and model show that there is no significant relation between economic freedom and death of COVID-19.


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## Body

## 1. Introduction

Due to COVID-19 pandemic, there are many fatalities across the world. Many countries are baffled by whether to open the market or impose lockdown [1–3]. It creates a huge chaos in either economic or social stability [4, 5]. This motivates us to study the relation between economic freedom and the death rate or tolls of COVID-19. We locate 164 countries from some datasets [6, 7]—because some of the countries lack statistics of either the economic freedom or the death information regarding COVID-19. Then, we use a series of mathematical and statistical approaches to reach a conclusion. For the mathematical part, we define a new concept of metric d which could measure the difference between the scoring structures—this is hardly the case if one adopts the usual Euclidean metric. For reference purpose, one fixes the referential structure e⟶ (or scoring system) first. Then, one could compute the distances between all the (sampled) multivalued data N points v⟶i:1≤i≤N and I, i.e., de⟶,v⟶i:1≤i≤N. Based on these distances, we could then create an ordering for v⟶i:1≤i≤N with respect to the referential structure e⟶.


## 2. Modelling

### 2.1. Notations and Symbols

For a vectorw⟶, we use w⟶ to denote its length; for any set H, we use H to denote its size (cardinality). Moreover, we use w⟶j to denote the j-th element in w⟶. Let b⟶ denote a binary vector, i.e., each element in b⟶ is either 0 or 1. Let Bk denote the set of all the binary vectors with total length k. Let ℂ=C1,C2,…,Cm be a set of countries. Let Aef=A1,A2,…,An be a set of attributes of economic freedom (regarded as independent variables). Let Bj be a set of result (regarded as dependent variables). Each time we fix one Bj to study the relation between the attributes and Bj. In this article, we restrict our attribute values to be numerical numbers. The theoretical table is shown in Table 1, and for the actual forms, one could refer to Sections 3.2.1 and 3.2.2.Table 1
Independent-dependent analysis.
CountriesA1A2…ApB1B2…BqC1a11a12…a1pb11b12…B1qC2a21a22…a2pb21b22…b2q…Cmam1am2…ampbm1bm2…bmqWe use the notationsCi⟶=ai1,ai2,…,aim; Ai⟶=a1i,a2i,…,ami; and Bi⟶=b1i,b2i,…,bmi.


### 2.2. Binary Subvectors and Norm

Definition 1.
(subvectors). Supposeb⟶ is a binary vector. We use Subb⟶ to denote all its truncated subvectors consisting of only 1.Example 1.
Supposeb⟶=1,0,1,0,0,1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0. Then, Subb⟶=1,1,1,1,1,1,1,1,1,1,1,1,1.We simply abbreviate it asSubb⟶=1111131211121211. Indeed Subb⟶ reveals the structure of an independent-dependent variable relation.Definition 2.
(binary norm). For any binary vectorb⟶=b1,b2,…,bk with Subb⟶=1n11n2,…,1nt, define a binary norm b⟶=20+21+⋯+2n1−1+20+21+…+2n2−1+⋯+20+21+⋯+2nt−1.One could, according to real situations, adopt other numbers (for example, replace 2 with other numbers) or other forms other than the one provided here.Claim 1.
b⟶=2n1+2n2+⋯+2nt−t.Proof.
It follows immediately from the definition.Definition 3.
(linear ordering onBk). b⟶1≥b⟶2 if and only if b⟶1≥b⟶2, for all b⟶1,b⟶2∈Bk.Example 2.
Ifb⟶1=1,0,1,1,1,0,0,1,1,0,1,0,1,b⟶2=1,0,0,0,0,1,1,0,0,1,1,1,1, then b⟶1=20⋅1+20⋅1+21⋅1+22⋅1+20⋅1+21⋅1+20⋅1+20⋅1=13 and b⟶2=20⋅1+20⋅1+21⋅1+20⋅1+21⋅1+22⋅1+23⋅1=19. Thus, b⟶2≤b⟶1.Remark 1.
A binary norm indeed serves an important technique in revealing the relation between dependent and independent variables. Given two pairsx1,y1 and x2,y2 of numerical data with x1≠x2, if x2−x1⋅y2−y1>0 (i.e., they act proportionally), we associate it with a value 1 to indicate such relation and 0, otherwise (i.e., they act inversely). Such mechanism gives a way to look into the fundamental relation between X and Y variables. This kind of analysis is in particular useful when the precision of the data is questionable or when the actual numbers are unknown or more suitable to be interpreted via ranks.Example 3.
(sign vector). SupposeD=2,4,3,2,5,8,7,9,4,2,3,8, a set of ordered vectors. Then, we could associate D with a sign vector v⟶=0,1,1,1,0 via Remark 1.Definition 4.
(relational vector). Suppose thatb⟶ is a sign vector; we associate it with a relational vector Relb⟶ whose i-th element is assigned 1 iff b⟶i=b⟶i+1 and 0, otherwise.Example 4.
Let us continue with Example3. We could compute its relational vector Relv⟶=0,1,1,0, and thus SubRelv⟶=12 and SubRelv⟶=3. The higher the value of the norm is, the closer the relation between the dependent and independent variables is.Definition 5.
(equivalence relation∼). For all b⟶1,b⟶2∈Bk, b⟶1∼b⟶2 iff b⟶1=b⟶2.LetBk#=b⟶:b⟶∈Bk. One observes that ∼ partitions Bk. If p∈Bk#, we use p to denote the equivalence class whose elements’ norms are all p.


### 2.3. Probability Distribution

SupposeBk=0,1k is the sampling population. Define a statistic BN on Bk by its binary norm. The range for BN is Bk#. Define a counting ρ:Bk#⟶ℕ by ρx=b⟶∈Bk:b⟶=x. Now, we could define the probability distribution for BN by prob:Bk#⟶0,1 by(1)probu=ρu∑h∈Ranρh.One observes that(2)probu=u∑h∈Ranh.This probability distribution reveals the relation between the independent variables and the dependent variables. This would serve our theoretical distribution for our statistical testingH0: the economic freedom and the death of COVID-19 has no significant relation, i.e., the economic freedom has no great impact on the death of COVID-19. For a concrete construction of such probability distribution, one could refer to Section 6.1.


### 2.4. Metric

A metric or a distance function is a non-negative functiond on X×X satisfying identity, symmetry, and triangle properties. In this article, it suffices to define a metric on a closed interval of real number. Fix I=a,b⊆ℝ, where a,b∈ℝ and a<b. Let v⟶ be a finite vector whose first element is a, last element is b, and all the other elements are incrementally increased and lie between a and b. Let FINa,b be the set of all such vectors. Let v⟶=a,v2,…,vm−1,b,w⟶=a,w2,w3,…,wn−1,b∈Fina,b be arbitrary. Let v⟶⊓w⟶ denote the vector q=a,q1,q2,…,qh−1,b whose elements are the projections from v⟶ and w⟶. One observes that FINa,b is closed under ⊓.Definition 6.
(atomic norm)v⟶E=(3)v2−a2+v3−v22+v4−v32+⋯vm−2−vm−12+b−vm−12.Definition 7.
(metric). Defined:FINa,b×FINa,b⟶ℝ+ by(4)dv⟶,w⟶=v⟶E+w⟶E2−v⟶⊓w⟶E.Example 5.
Suppose the closed intervalI=0,20 and v⟶=0,2,4,8,19,20 and w⟶=0,1,4,6,12,14,15,20. Then, v⟶⊓w⟶=0,1,2,4,6,8,12,14,15,19,20. Hence, the norm v⟶E=22+22+42+112+12=146; the norm w⟶=12+32+22+62+22+12+52=80; and v⟶⊓w⟶E=52. Thus, dv⟶,w⟶=146+80/2−52=3.30.Claim 2.
d is a metric on FINa,b.Proof.
This can be shown by the definitions and some techniques.This metric will be used in Section3.3. This metric basically measures the differences between the structures of the attributes in the scoring system. The more similar the structures are, the lower the distances are. Unlike the static Euclidean distance, this metric takes the interval structures into consideration.


### 2.5. Procedures

Let us summarise the whole procedure of our modelling for the sake of data analysis. Lete⟶=100,100,100,100,…,100,100. Let DeathCi denote the death rate (or tolls, depending on the context) for the country i.(1)
Define a metricd on a real interval, in particular the transformed interval, an interval for attribute values which lie between 0 and 100, I=0,1200⊆ℝ for the range of attribute values of economic freedom, and calculate dI^,C⟶i:1≤i≤m (one could refer to Section 3.3).(2)
Rankℂ via the sorted distances with a rank function γ100:ℂ⟶1,2,…,m in which γICi≥γICj iff dI⟶,C⟶i≥dI⟶,C⟶i.(3)
Rankℂ via the sorted distance with a rank function γ88 in which γ88Ci≥γ88Cj iff DeathCi≥DeathCj.(4)
Form the vectorv⟶=γ100°γ88−1ll=1m.(5)
Convertv⟶ into a sign vector sgv⟶:=χv⟶2−v⟶1,χv⟶3−v⟶2,…,χv⟶m−v⟶m−1, where χa=1 if a>0 and χa=0 if a<0.(6)
Construct the probability distribution for the quotient spaceBk/∼.(7)
Perform statistical testing by locating the position ofv⟶ and significant level for the batch of country.(8)
Apply the Monte Carlo approach on the sampled batches of countries repeatedly.(9)
With the threshold probability 0.5, based on binary distribution for the whole spectrum of statistical testing, perform the overall statistical testing.(10)
Draw a conclusion for the relation betweenγ100 and γ88.


## 2.1. Notations and Symbols

For a vectorw⟶, we use w⟶ to denote its length; for any set H, we use H to denote its size (cardinality). Moreover, we use w⟶j to denote the j-th element in w⟶. Let b⟶ denote a binary vector, i.e., each element in b⟶ is either 0 or 1. Let Bk denote the set of all the binary vectors with total length k. Let ℂ=C1,C2,…,Cm be a set of countries. Let Aef=A1,A2,…,An be a set of attributes of economic freedom (regarded as independent variables). Let Bj be a set of result (regarded as dependent variables). Each time we fix one Bj to study the relation between the attributes and Bj. In this article, we restrict our attribute values to be numerical numbers. The theoretical table is shown in Table 1, and for the actual forms, one could refer to Sections 3.2.1 and 3.2.2.Table 1
Independent-dependent analysis.
CountriesA1A2…ApB1B2…BqC1a11a12…a1pb11b12…B1qC2a21a22…a2pb21b22…b2q…Cmam1am2…ampbm1bm2…bmqWe use the notationsCi⟶=ai1,ai2,…,aim; Ai⟶=a1i,a2i,…,ami; and Bi⟶=b1i,b2i,…,bmi.


## 2.2. Binary Subvectors and Norm

Definition 1.
(subvectors). Supposeb⟶ is a binary vector. We use Subb⟶ to denote all its truncated subvectors consisting of only 1.Example 1.
Supposeb⟶=1,0,1,0,0,1,1,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0. Then, Subb⟶=1,1,1,1,1,1,1,1,1,1,1,1,1.We simply abbreviate it asSubb⟶=1111131211121211. Indeed Subb⟶ reveals the structure of an independent-dependent variable relation.Definition 2.
(binary norm). For any binary vectorb⟶=b1,b2,…,bk with Subb⟶=1n11n2,…,1nt, define a binary norm b⟶=20+21+⋯+2n1−1+20+21+…+2n2−1+⋯+20+21+⋯+2nt−1.One could, according to real situations, adopt other numbers (for example, replace 2 with other numbers) or other forms other than the one provided here.Claim 1.
b⟶=2n1+2n2+⋯+2nt−t.Proof.
It follows immediately from the definition.Definition 3.
(linear ordering onBk). b⟶1≥b⟶2 if and only if b⟶1≥b⟶2, for all b⟶1,b⟶2∈Bk.Example 2.
Ifb⟶1=1,0,1,1,1,0,0,1,1,0,1,0,1,b⟶2=1,0,0,0,0,1,1,0,0,1,1,1,1, then b⟶1=20⋅1+20⋅1+21⋅1+22⋅1+20⋅1+21⋅1+20⋅1+20⋅1=13 and b⟶2=20⋅1+20⋅1+21⋅1+20⋅1+21⋅1+22⋅1+23⋅1=19. Thus, b⟶2≤b⟶1.Remark 1.
A binary norm indeed serves an important technique in revealing the relation between dependent and independent variables. Given two pairsx1,y1 and x2,y2 of numerical data with x1≠x2, if x2−x1⋅y2−y1>0 (i.e., they act proportionally), we associate it with a value 1 to indicate such relation and 0, otherwise (i.e., they act inversely). Such mechanism gives a way to look into the fundamental relation between X and Y variables. This kind of analysis is in particular useful when the precision of the data is questionable or when the actual numbers are unknown or more suitable to be interpreted via ranks.Example 3.
(sign vector). SupposeD=2,4,3,2,5,8,7,9,4,2,3,8, a set of ordered vectors. Then, we could associate D with a sign vector v⟶=0,1,1,1,0 via Remark 1.Definition 4.
(relational vector). Suppose thatb⟶ is a sign vector; we associate it with a relational vector Relb⟶ whose i-th element is assigned 1 iff b⟶i=b⟶i+1 and 0, otherwise.Example 4.
Let us continue with Example3. We could compute its relational vector Relv⟶=0,1,1,0, and thus SubRelv⟶=12 and SubRelv⟶=3. The higher the value of the norm is, the closer the relation between the dependent and independent variables is.Definition 5.
(equivalence relation∼). For all b⟶1,b⟶2∈Bk, b⟶1∼b⟶2 iff b⟶1=b⟶2.LetBk#=b⟶:b⟶∈Bk. One observes that ∼ partitions Bk. If p∈Bk#, we use p to denote the equivalence class whose elements’ norms are all p.


## 2.3. Probability Distribution

SupposeBk=0,1k is the sampling population. Define a statistic BN on Bk by its binary norm. The range for BN is Bk#. Define a counting ρ:Bk#⟶ℕ by ρx=b⟶∈Bk:b⟶=x. Now, we could define the probability distribution for BN by prob:Bk#⟶0,1 by(1)probu=ρu∑h∈Ranρh.One observes that(2)probu=u∑h∈Ranh.This probability distribution reveals the relation between the independent variables and the dependent variables. This would serve our theoretical distribution for our statistical testingH0: the economic freedom and the death of COVID-19 has no significant relation, i.e., the economic freedom has no great impact on the death of COVID-19. For a concrete construction of such probability distribution, one could refer to Section 6.1.


## 2.4. Metric

A metric or a distance function is a non-negative functiond on X×X satisfying identity, symmetry, and triangle properties. In this article, it suffices to define a metric on a closed interval of real number. Fix I=a,b⊆ℝ, where a,b∈ℝ and a<b. Let v⟶ be a finite vector whose first element is a, last element is b, and all the other elements are incrementally increased and lie between a and b. Let FINa,b be the set of all such vectors. Let v⟶=a,v2,…,vm−1,b,w⟶=a,w2,w3,…,wn−1,b∈Fina,b be arbitrary. Let v⟶⊓w⟶ denote the vector q=a,q1,q2,…,qh−1,b whose elements are the projections from v⟶ and w⟶. One observes that FINa,b is closed under ⊓.Definition 6.
(atomic norm)v⟶E=(3)v2−a2+v3−v22+v4−v32+⋯vm−2−vm−12+b−vm−12.Definition 7.
(metric). Defined:FINa,b×FINa,b⟶ℝ+ by(4)dv⟶,w⟶=v⟶E+w⟶E2−v⟶⊓w⟶E.Example 5.
Suppose the closed intervalI=0,20 and v⟶=0,2,4,8,19,20 and w⟶=0,1,4,6,12,14,15,20. Then, v⟶⊓w⟶=0,1,2,4,6,8,12,14,15,19,20. Hence, the norm v⟶E=22+22+42+112+12=146; the norm w⟶=12+32+22+62+22+12+52=80; and v⟶⊓w⟶E=52. Thus, dv⟶,w⟶=146+80/2−52=3.30.Claim 2.
d is a metric on FINa,b.Proof.
This can be shown by the definitions and some techniques.This metric will be used in Section3.3. This metric basically measures the differences between the structures of the attributes in the scoring system. The more similar the structures are, the lower the distances are. Unlike the static Euclidean distance, this metric takes the interval structures into consideration.


## 2.5. Procedures

Let us summarise the whole procedure of our modelling for the sake of data analysis. Lete⟶=100,100,100,100,…,100,100. Let DeathCi denote the death rate (or tolls, depending on the context) for the country i.(1)
Define a metricd on a real interval, in particular the transformed interval, an interval for attribute values which lie between 0 and 100, I=0,1200⊆ℝ for the range of attribute values of economic freedom, and calculate dI^,C⟶i:1≤i≤m (one could refer to Section 3.3).(2)
Rankℂ via the sorted distances with a rank function γ100:ℂ⟶1,2,…,m in which γICi≥γICj iff dI⟶,C⟶i≥dI⟶,C⟶i.(3)
Rankℂ via the sorted distance with a rank function γ88 in which γ88Ci≥γ88Cj iff DeathCi≥DeathCj.(4)
Form the vectorv⟶=γ100°γ88−1ll=1m.(5)
Convertv⟶ into a sign vector sgv⟶:=χv⟶2−v⟶1,χv⟶3−v⟶2,…,χv⟶m−v⟶m−1, where χa=1 if a>0 and χa=0 if a<0.(6)
Construct the probability distribution for the quotient spaceBk/∼.(7)
Perform statistical testing by locating the position ofv⟶ and significant level for the batch of country.(8)
Apply the Monte Carlo approach on the sampled batches of countries repeatedly.(9)
With the threshold probability 0.5, based on binary distribution for the whole spectrum of statistical testing, perform the overall statistical testing.(10)
Draw a conclusion for the relation betweenγ100 and γ88.


## 3. Data Analysis

Following the procedures in Section2.5, we start to collect, analyse, and produce a report via data analysis. Since the data are huge and hard to handle by the one-off approach, we resort to the sampling technique and reach a conclusion via statistical testing.


### 3.1. Sampling

The raw data consist of 164 countries (we use 1 to 164 to name the countries) up to 2020, June 27th. Since the size is too huge, we apply the Monte Carlo approach to sample the 164 countries. We do 20 times (or 20 batches: S1 to S20) sampling with 25 countries over the 164 countries per sampling. The sampled batches are listed in Tables 2 and 3.Table 2
20 sampled batches—S1 to S10.
OrderS1S2S3S4S5S6S7S8S9S1016825691027657256641632141127939855857515115019321955561411515911265104129413045735130136911751271715174119571281396952699151338920160147100271878914156261249519271138882431327335118122835365912876448415329129168410510108284870150159471101501111262126671517111813415626129213161219086918789161139810466980893910752821418119845037507152212715148128399784138111113257161241213434556154815291711895927591158101662018321698181134112546127116197692268759714411356382014428514285324670974121416013748612176140922213710314413738758684102128238512053213212413211931724781631171221111229974163222552118627766193512388103Table 3
20 sampled batches—S11 to S20.
OrderS11S12S13S14S15S16S17S18S19S20176918359641191291541537223124536346123882305532915112624143137635431194121261295553108122414816357365914386541524076155615786181005976769133187495410250406120198686811950855215693891469991587104743215270146145122104887440681112714357162111041187115361012513426251299671257913585136701011561314259158521563663813114714136139201593937110613110154143576996306720201341611514815110850665014267917151565449275153546344187715273647162269825157191261690136154124132567042010882938713295891518520219539161981381384411171672260374421621207611311815323366165412069141108849724142861091213484741148257410103119157136735258136


### 3.2. Sampled Data

#### 3.2.1. Economic Freedom

Corresponding to the form listed in Table1, we associate ℂ with S1 and define Aef=A1,A2,…,A12, where A1≡Property Rights, A2≡Judicial Effectiveness, A3≡Government Integrity, A4≡Tax Burden, A5≡Government Spending, A6≡Fiscal Health, A7≡Business Freedom, A8≡Labor Freedom, A9≡Monetary Freedom, A10≡Trade Freedom, A11≡Investment Freedom, and A12≡Financial Freedom. The attribute values are based on a 100-point scoring system [6]. Due to the limitation of space, we list only the first sampling (or S1) regarding its attributes of economic freedom in Table 4. We omit the other 19 similar tables of this form. Aef serves as the set of our independent variables.Table 4
Sample one for economic freedom.
S1A1A2A3A4A5A6A7A8A9A10A11A126864.845.747.579.934.583.660.264.679.986.4807014133.720.825.586.194.512.453.56077525202157.346.745.670.454.64.660.549.577.267.8605012964.672.349.699.861.819.366.663.38175.4455012769.862.641.876.980.683.876.766.48273.265409958.334.736.776.179.387.56758.470.987.675608986.474.490.364.145.49966.845.376.486.49580257.13338.885.974.686.365.752.181.288.470701284126.537.488.377.17364.843.468.164.2603010893.379.193.97157.898.390.486.78792.2808011262.542.742.291.57187.780.66777.786.265609243.142.124.87971.723.641.962.869.175.45050875.862.653.391.582.179.382.560.273.888.280701820.111.223.186.354.214.258.352.969.967.8154014859.54843.480.785.996.48363.77483556012472.556.155.190.370.485.658.66378.186.47050148.33024.891.479.299.954.761.6816610103269.961.173.476.480.890.57564.785.28985707662.150.546.88074.880.277.77477.768.480501484.562.580.246.717.27775.261.180.586.485704186.384.6934219.797.788.786.284.686.4908013758.43846.663.767.4646258.875.975.845508544.630.82590.872.5045.647.875.677.460507864.854.649.691.873.555.960.152.577.681.270605236.545.129.477.490.879.248.657.662.760.83520


#### 3.2.2. COVID-19

Now we start to introduce the dependent variables. Indeed we tackle an individual dependent variable each time. Since the data are huge, we only extract the data [7] for sampling one (or S1) as shown in Table 5. Corresponding to the form listed in Table 1, we associate ℂ with S1 and define B1≡ Total Confirmed COVID-19 Cases, B2≡ Death Toll of COVID-19, B3≡ Total Recovered COVID-19 Cases, and B4≡ Population of the Countries. Due to the limitation of space, we list only the first sampling (or S1) regarding its dependent variables. We omit the other 19 similar tables of this form. Moreover, in the later analysis, we only take and fix B2 as our dependent variable. If the readers are interested in other dependent variables (or B1, B3, or other mixed forms), they could simply follow the same approach provided in this article.Table 5
Sample one for COVID-19.
S1ℂB1B2B3B468Hungary412757826639660521141Sudan925757240144382854321Brazil128005456109697526212541690129Senegal635498419316734279127Sao Tome and Principe7121321921908799Mexico2083922577912056212891450789Luxembourg417311039686258102Albania22695112982877821128Saudi Arabia174577147412047134805142108New Zealand15202214845002100112North Macedonia57582682206208337592Malawi1005132601911928198Mauritius34110326127174918Bolivia28503913733811670618148Thailand316258304069798329124Romania25697157918181192383211Afghanistan30451683103063891099632Chile26336050682234311911415376Jamaica68610539296103314Belgium611069731169181158910241Denmark12675604115085792000137South Africa1245902340641115929780785Lebanon1697331144682562778Jordan110498301020180052Ethiopia5425891688114903773


### 3.3. Metric

Since we have defined an interval metric in Section2.4, we could apply it over here. Here we measure the distance between every sampled data and the fixed reference vector e⟶=100,200,…,1100,1200. We construct the distances for the 164 countries based on economic freedom (for example, the data of sample one could be referred from Table 4) in Tables 6 and 7. Since all the data are presented in the form of 100-point score for the attribute values in Table 4, we need to transform the values in the table to the interval I=0,1200. For example, the reference vector e⟶ (we still use e⟶ to represent to newly transformed vector) will be e⟶=0,100,200,300,…,1100,1200. Each country C sampled in S1 will be transformed into C⟶, for example, C¯⟶11≡68⟶=0,64.8,145.7,247.5,379.9,…,1170,1200 are the converted data for the first country sampled in the first sampling or country 68. The economic freedom vector for each sampled country is converted by the same way. The converted data are not tabulated. Then, we apply d in Section 2.4 on the converted data and repeat the whole processes for other samplings. The complete results regarding the distance for the 20 sampled countries are presented in Tables 6 and 7. The i,j cell in the tables means the value de⟶,C¯⟶ij, where C¯ij denotes the i-th country sampled in j-th sampling and C¯⟶ij denotes the converted data for C¯ij.Table 6
Distance function for 20 samplings—S1 to S10.
S1S2S3S4S5S6S7S8S9S1061.080.182.274.278.373.253.959.266.872.276.276.875.472.473.684.072.883.480.471.370.772.471.159.285.168.666.562.373.274.280.882.171.482.364.977.274.385.770.265.076.871.883.478.572.867.176.978.982.280.775.083.469.765.584.449.267.777.478.375.865.585.157.371.371.172.471.378.374.461.880.470.474.868.777.265.067.867.357.573.276.969.581.574.873.171.880.873.174.868.173.361.360.171.480.483.270.272.372.780.462.373.871.976.583.464.265.077.657.371.363.074.949.977.871.980.182.662.765.582.372.474.274.082.278.465.566.045.780.772.575.872.874.879.954.179.964.280.770.778.368.876.966.065.174.870.474.469.274.867.171.177.877.371.482.359.283.260.183.271.871.375.872.463.072.882.671.675.433.684.474.373.172.475.874.482.168.874.076.874.569.563.071.362.782.664.959.474.459.274.085.177.784.059.784.074.374.071.465.182.182.166.071.354.160.172.070.769.564.263.067.782.759.467.774.072.880.174.882.376.984.073.357.580.474.871.174.872.860.964.967.772.265.067.869.267.875.078.572.268.280.765.073.878.633.671.377.272.361.882.7Table 7
Distance function for 20 samplings—S11 to S20.
S11S12S13S14S15S16S17S18S19S2069.582.667.382.666.872.880.881.183.254.182.371.157.583.274.072.371.672.571.473.671.883.471.974.452.967.749.977.270.472.868.771.980.873.657.573.367.890.368.872.268.773.270.252.980.171.680.649.169.558.962.980.175.877.482.669.564.982.232.375.859.671.682.379.949.149.973.371.371.649.961.072.879.984.080.757.375.465.573.575.083.262.778.878.574.380.671.473.580.167.860.171.678.549.161.069.278.352.967.182.078.884.062.768.680.775.480.177.671.380.175.076.568.883.974.584.085.771.475.457.359.782.671.680.757.371.433.674.074.967.785.778.984.466.566.054.172.772.060.974.282.170.467.182.272.771.476.584.484.477.668.668.883.473.379.933.679.959.749.983.983.459.271.659.678.374.157.571.683.281.578.683.278.380.772.382.071.372.480.162.971.973.171.985.781.171.174.859.271.490.373.372.575.462.774.872.465.583.484.084.472.466.082.372.478.278.281.569.264.276.566.054.181.570.773.873.369.574.465.073.180.749.973.171.673.382.276.273.374.865.171.377.780.184.768.777.674.864.982.168.878.574.282.772.862.985.768.780.782.985.7


## 3.1. Sampling

The raw data consist of 164 countries (we use 1 to 164 to name the countries) up to 2020, June 27th. Since the size is too huge, we apply the Monte Carlo approach to sample the 164 countries. We do 20 times (or 20 batches: S1 to S20) sampling with 25 countries over the 164 countries per sampling. The sampled batches are listed in Tables 2 and 3.Table 2
20 sampled batches—S1 to S10.
OrderS1S2S3S4S5S6S7S8S9S1016825691027657256641632141127939855857515115019321955561411515911265104129413045735130136911751271715174119571281396952699151338920160147100271878914156261249519271138882431327335118122835365912876448415329129168410510108284870150159471101501111262126671517111813415626129213161219086918789161139810466980893910752821418119845037507152212715148128399784138111113257161241213434556154815291711895927591158101662018321698181134112546127116197692268759714411356382014428514285324670974121416013748612176140922213710314413738758684102128238512053213212413211931724781631171221111229974163222552118627766193512388103Table 3
20 sampled batches—S11 to S20.
OrderS11S12S13S14S15S16S17S18S19S20176918359641191291541537223124536346123882305532915112624143137635431194121261295553108122414816357365914386541524076155615786181005976769133187495410250406120198686811950855215693891469991587104743215270146145122104887440681112714357162111041187115361012513426251299671257913585136701011561314259158521563663813114714136139201593937110613110154143576996306720201341611514815110850665014267917151565449275153546344187715273647162269825157191261690136154124132567042010882938713295891518520219539161981381384411171672260374421621207611311815323366165412069141108849724142861091213484741148257410103119157136735258136


## 3.2. Sampled Data

### 3.2.1. Economic Freedom

Corresponding to the form listed in Table1, we associate ℂ with S1 and define Aef=A1,A2,…,A12, where A1≡Property Rights, A2≡Judicial Effectiveness, A3≡Government Integrity, A4≡Tax Burden, A5≡Government Spending, A6≡Fiscal Health, A7≡Business Freedom, A8≡Labor Freedom, A9≡Monetary Freedom, A10≡Trade Freedom, A11≡Investment Freedom, and A12≡Financial Freedom. The attribute values are based on a 100-point scoring system [6]. Due to the limitation of space, we list only the first sampling (or S1) regarding its attributes of economic freedom in Table 4. We omit the other 19 similar tables of this form. Aef serves as the set of our independent variables.Table 4
Sample one for economic freedom.
S1A1A2A3A4A5A6A7A8A9A10A11A126864.845.747.579.934.583.660.264.679.986.4807014133.720.825.586.194.512.453.56077525202157.346.745.670.454.64.660.549.577.267.8605012964.672.349.699.861.819.366.663.38175.4455012769.862.641.876.980.683.876.766.48273.265409958.334.736.776.179.387.56758.470.987.675608986.474.490.364.145.49966.845.376.486.49580257.13338.885.974.686.365.752.181.288.470701284126.537.488.377.17364.843.468.164.2603010893.379.193.97157.898.390.486.78792.2808011262.542.742.291.57187.780.66777.786.265609243.142.124.87971.723.641.962.869.175.45050875.862.653.391.582.179.382.560.273.888.280701820.111.223.186.354.214.258.352.969.967.8154014859.54843.480.785.996.48363.77483556012472.556.155.190.370.485.658.66378.186.47050148.33024.891.479.299.954.761.6816610103269.961.173.476.480.890.57564.785.28985707662.150.546.88074.880.277.77477.768.480501484.562.580.246.717.27775.261.180.586.485704186.384.6934219.797.788.786.284.686.4908013758.43846.663.767.4646258.875.975.845508544.630.82590.872.5045.647.875.677.460507864.854.649.691.873.555.960.152.577.681.270605236.545.129.477.490.879.248.657.662.760.83520


### 3.2.2. COVID-19

Now we start to introduce the dependent variables. Indeed we tackle an individual dependent variable each time. Since the data are huge, we only extract the data [7] for sampling one (or S1) as shown in Table 5. Corresponding to the form listed in Table 1, we associate ℂ with S1 and define B1≡ Total Confirmed COVID-19 Cases, B2≡ Death Toll of COVID-19, B3≡ Total Recovered COVID-19 Cases, and B4≡ Population of the Countries. Due to the limitation of space, we list only the first sampling (or S1) regarding its dependent variables. We omit the other 19 similar tables of this form. Moreover, in the later analysis, we only take and fix B2 as our dependent variable. If the readers are interested in other dependent variables (or B1, B3, or other mixed forms), they could simply follow the same approach provided in this article.Table 5
Sample one for COVID-19.
S1ℂB1B2B3B468Hungary412757826639660521141Sudan925757240144382854321Brazil128005456109697526212541690129Senegal635498419316734279127Sao Tome and Principe7121321921908799Mexico2083922577912056212891450789Luxembourg417311039686258102Albania22695112982877821128Saudi Arabia174577147412047134805142108New Zealand15202214845002100112North Macedonia57582682206208337592Malawi1005132601911928198Mauritius34110326127174918Bolivia28503913733811670618148Thailand316258304069798329124Romania25697157918181192383211Afghanistan30451683103063891099632Chile26336050682234311911415376Jamaica68610539296103314Belgium611069731169181158910241Denmark12675604115085792000137South Africa1245902340641115929780785Lebanon1697331144682562778Jordan110498301020180052Ethiopia5425891688114903773


## 3.2.1. Economic Freedom

Corresponding to the form listed in Table1, we associate ℂ with S1 and define Aef=A1,A2,…,A12, where A1≡Property Rights, A2≡Judicial Effectiveness, A3≡Government Integrity, A4≡Tax Burden, A5≡Government Spending, A6≡Fiscal Health, A7≡Business Freedom, A8≡Labor Freedom, A9≡Monetary Freedom, A10≡Trade Freedom, A11≡Investment Freedom, and A12≡Financial Freedom. The attribute values are based on a 100-point scoring system [6]. Due to the limitation of space, we list only the first sampling (or S1) regarding its attributes of economic freedom in Table 4. We omit the other 19 similar tables of this form. Aef serves as the set of our independent variables.Table 4
Sample one for economic freedom.
S1A1A2A3A4A5A6A7A8A9A10A11A126864.845.747.579.934.583.660.264.679.986.4807014133.720.825.586.194.512.453.56077525202157.346.745.670.454.64.660.549.577.267.8605012964.672.349.699.861.819.366.663.38175.4455012769.862.641.876.980.683.876.766.48273.265409958.334.736.776.179.387.56758.470.987.675608986.474.490.364.145.49966.845.376.486.49580257.13338.885.974.686.365.752.181.288.470701284126.537.488.377.17364.843.468.164.2603010893.379.193.97157.898.390.486.78792.2808011262.542.742.291.57187.780.66777.786.265609243.142.124.87971.723.641.962.869.175.45050875.862.653.391.582.179.382.560.273.888.280701820.111.223.186.354.214.258.352.969.967.8154014859.54843.480.785.996.48363.77483556012472.556.155.190.370.485.658.66378.186.47050148.33024.891.479.299.954.761.6816610103269.961.173.476.480.890.57564.785.28985707662.150.546.88074.880.277.77477.768.480501484.562.580.246.717.27775.261.180.586.485704186.384.6934219.797.788.786.284.686.4908013758.43846.663.767.4646258.875.975.845508544.630.82590.872.5045.647.875.677.460507864.854.649.691.873.555.960.152.577.681.270605236.545.129.477.490.879.248.657.662.760.83520


## 3.2.2. COVID-19

Now we start to introduce the dependent variables. Indeed we tackle an individual dependent variable each time. Since the data are huge, we only extract the data [7] for sampling one (or S1) as shown in Table 5. Corresponding to the form listed in Table 1, we associate ℂ with S1 and define B1≡ Total Confirmed COVID-19 Cases, B2≡ Death Toll of COVID-19, B3≡ Total Recovered COVID-19 Cases, and B4≡ Population of the Countries. Due to the limitation of space, we list only the first sampling (or S1) regarding its dependent variables. We omit the other 19 similar tables of this form. Moreover, in the later analysis, we only take and fix B2 as our dependent variable. If the readers are interested in other dependent variables (or B1, B3, or other mixed forms), they could simply follow the same approach provided in this article.Table 5
Sample one for COVID-19.
S1ℂB1B2B3B468Hungary412757826639660521141Sudan925757240144382854321Brazil128005456109697526212541690129Senegal635498419316734279127Sao Tome and Principe7121321921908799Mexico2083922577912056212891450789Luxembourg417311039686258102Albania22695112982877821128Saudi Arabia174577147412047134805142108New Zealand15202214845002100112North Macedonia57582682206208337592Malawi1005132601911928198Mauritius34110326127174918Bolivia28503913733811670618148Thailand316258304069798329124Romania25697157918181192383211Afghanistan30451683103063891099632Chile26336050682234311911415376Jamaica68610539296103314Belgium611069731169181158910241Denmark12675604115085792000137South Africa1245902340641115929780785Lebanon1697331144682562778Jordan110498301020180052Ethiopia5425891688114903773


## 3.3. Metric

Since we have defined an interval metric in Section2.4, we could apply it over here. Here we measure the distance between every sampled data and the fixed reference vector e⟶=100,200,…,1100,1200. We construct the distances for the 164 countries based on economic freedom (for example, the data of sample one could be referred from Table 4) in Tables 6 and 7. Since all the data are presented in the form of 100-point score for the attribute values in Table 4, we need to transform the values in the table to the interval I=0,1200. For example, the reference vector e⟶ (we still use e⟶ to represent to newly transformed vector) will be e⟶=0,100,200,300,…,1100,1200. Each country C sampled in S1 will be transformed into C⟶, for example, C¯⟶11≡68⟶=0,64.8,145.7,247.5,379.9,…,1170,1200 are the converted data for the first country sampled in the first sampling or country 68. The economic freedom vector for each sampled country is converted by the same way. The converted data are not tabulated. Then, we apply d in Section 2.4 on the converted data and repeat the whole processes for other samplings. The complete results regarding the distance for the 20 sampled countries are presented in Tables 6 and 7. The i,j cell in the tables means the value de⟶,C¯⟶ij, where C¯ij denotes the i-th country sampled in j-th sampling and C¯⟶ij denotes the converted data for C¯ij.Table 6
Distance function for 20 samplings—S1 to S10.
S1S2S3S4S5S6S7S8S9S1061.080.182.274.278.373.253.959.266.872.276.276.875.472.473.684.072.883.480.471.370.772.471.159.285.168.666.562.373.274.280.882.171.482.364.977.274.385.770.265.076.871.883.478.572.867.176.978.982.280.775.083.469.765.584.449.267.777.478.375.865.585.157.371.371.172.471.378.374.461.880.470.474.868.777.265.067.867.357.573.276.969.581.574.873.171.880.873.174.868.173.361.360.171.480.483.270.272.372.780.462.373.871.976.583.464.265.077.657.371.363.074.949.977.871.980.182.662.765.582.372.474.274.082.278.465.566.045.780.772.575.872.874.879.954.179.964.280.770.778.368.876.966.065.174.870.474.469.274.867.171.177.877.371.482.359.283.260.183.271.871.375.872.463.072.882.671.675.433.684.474.373.172.475.874.482.168.874.076.874.569.563.071.362.782.664.959.474.459.274.085.177.784.059.784.074.374.071.465.182.182.166.071.354.160.172.070.769.564.263.067.782.759.467.774.072.880.174.882.376.984.073.357.580.474.871.174.872.860.964.967.772.265.067.869.267.875.078.572.268.280.765.073.878.633.671.377.272.361.882.7Table 7
Distance function for 20 samplings—S11 to S20.
S11S12S13S14S15S16S17S18S19S2069.582.667.382.666.872.880.881.183.254.182.371.157.583.274.072.371.672.571.473.671.883.471.974.452.967.749.977.270.472.868.771.980.873.657.573.367.890.368.872.268.773.270.252.980.171.680.649.169.558.962.980.175.877.482.669.564.982.232.375.859.671.682.379.949.149.973.371.371.649.961.072.879.984.080.757.375.465.573.575.083.262.778.878.574.380.671.473.580.167.860.171.678.549.161.069.278.352.967.182.078.884.062.768.680.775.480.177.671.380.175.076.568.883.974.584.085.771.475.457.359.782.671.680.757.371.433.674.074.967.785.778.984.466.566.054.172.772.060.974.282.170.467.182.272.771.476.584.484.477.668.668.883.473.379.933.679.959.749.983.983.459.271.659.678.374.157.571.683.281.578.683.278.380.772.382.071.372.480.162.971.973.171.985.781.171.174.859.271.490.373.372.575.462.774.872.465.583.484.084.472.466.082.372.478.278.281.569.264.276.566.054.181.570.773.873.369.574.465.073.180.749.973.171.673.382.276.273.374.865.171.377.780.184.768.777.674.864.982.168.878.574.282.772.862.985.768.780.782.985.7


## 4. Absolute Reference

By the derived distances presented in Tables6 and 7, we could construct absolute references. The absolute references would server as the benchmarks for other internal structures. Let us use ℂs to denote the set of sampled countries in s-th sampling. Let C¯⟶si,C¯⟶sj∈ℂs be arbitrary.Definition 8.
(ordering of the sampled countries).C¯is≥C¯js iff de⟶,C¯⟶is≥de⟶,C¯⟶js.Based on this ordering, we could generate the absolute references (Tables8 and 9). Let us take S1 for example: C68>C112>C92>⋯>C41>C85>C14. From these absolute references (or ordering for the samplings), we could view the structure (or interval) difference between the ideal scoring (or e⟶) and real scoring results. Indeed, an absolute reference is a reference acting like ordering without specific scales. Such reference is useful when the precise values are unknown or when the precision of the data is questionable. In this article, we use relative distances between a country’s economic freedom and others to create such ordering.Table 8
Absolute references for 20 samplings—S1 to S10.
S1S2S3S4S5S6S7S8S9S10682863766160721076688112921565637561445615692921185314248717148537896014487771181125611778764892111118398731571374311797124891598388105148173989905714711114022761633313775122122769726219551221191151257089191241191731531391236429116262655124214791639812030703819191192182108621263113291581616365321098981326175461103899131951084954611365101818628435751308411311614112746182765811011321812712813267803213210084128128428412115035991341272721219374455012827271505225347759863574150521294144501514186139524141103692859112952691618515115169201591151102103141485451485151361520Table 9
Absolute references for 20 samplings—S11 to S20.
S11S12S13S14S15S16S17S18S19S204965340406666401336142378714314366143637485657491563753563115668878387531567142711551573912515968137897118157601489115157111122895797115431582139767311114814773124545464124761976122128126981230267043148765490119473705426163112616108965486170119298293551201231109830153126119182462951208285595162710046119132108146101086574743212084146849999101045013510893381311874675052132511411131016777428636138101673514513410413912969271342713425253686445950138505241444191102638615225154581622359161795216215269637915151038536691291511520151151151109154854420851361361120136591361364204


## 5. Ordering for COVID-19 Fatalities

Based on Table5 and other omitted tables, we start to construct the ordering (or ranking) based on the fatalities of COVID-19.Definition 9.
(ordering on fatalities).C¯is≥C¯js iff DeathC¯is≥DeathC¯js, where DeathC¯is is the death toll for i-th country sampled in s-th sampling.Based on this ordering, we have the results presented in Tables10 and 11. Let us take the cells in S1 for example: C78>C98>C76>⋯>C14>C99>C21.Table 10
Ordering for each batch based on death toll of COVID-19—S1 to S10.
S1S2S3S4S5S6S7S8S9S10784353679015158353117981311179820353510115207625126263511811815110222127151151691515791766926921769142150913916140921087698928416014713464150851272684488515984127572923987855613248150163148118625613250129871631615216842386519568482129163485059795256108962851078913013613288112423037379581123110381411013289801912847315268959597113131221138865416093746641144112527110315631116146746519182861812412271100891031284117745124125111971161241844121153717246941137120512211911599107113183212114473143275119156128141284613755292170662999119344575751581392110521143370278686272727Table 11
Ordering for each batch based on death toll of COVID-19—S11 to S20.
S11S12S13S14S15S16S17S18S19S204943834953101532043162151265369121622535101251261590989651671511312010467203664762642067121511266336697669254151161041083913484142151347691151159135108152981451631423910285628513213476147368757871323011010826148108561624501525056118104882875052371298257371364216110959123714663136951485052471361363813397601012959138958952847923659313615613893785156745997940156689306683710374685466191464441547454120614111314818165440466685431155778441003211144406122731241811514331201114115311511125143157120122618119291191581198612473143719999139275527137707058551578686211541192715470157


## 6. Norm and Probability

In this experiment, we only considerN=23 and construct its distribution accordingly. Hence, the domain is 0,123 and the range lies between 0 and 223−1=8388607 (indeed some of the values’ probability is 0). This section generalises Example 3. The higher the value is, the higher the impact of independent variables on dependent variable is.


### 6.1. Probability Distribution

We have already constructed the theoretical setting of probability distribution for our testing in Section2.3. Based on that framework and the data given, we could create the theoretical probability distribution prob in Figure 1.Figure 1
Theoretical distribution of binary norm.The (one-tailed) critical values for 5 and 10 percentages are 138 and 78 (via numerical computation), respectively; that is, if the sampled value is larger than the critical values, we should rejectHo: there is no significant relation between the economic freedom and death of COVID-19.


### 6.2. Real Results

In comparison with the absolute reference, we could generate the binary sign vectors for the real data from each samplingSj (or simply j) in Table 12—for the formula and explanation of sign vectors, one could refer to Section 2.2. However, in these 0 and 1 representations, it separates the proportional and inversely proportional relation between the economic freedom and death of COVID-19. To take all the factors into consideration, one further analyses the alternative behaviour of 0 and 1. If there are too many alternations between 0 and 1, it would indicate that there is a less relation between those two. On the other hand, if the alternative times are few, then it leads to the longer length of subvector consisting of pure 1. The alternative results are shown in Table 13.Table 12
Sign vectors.
1234567891011121314151617181920111010011111011110100110000100011010010111111110011011000110000001010001011100011001001111101000101011010100100110101100000010101100010101000110011101100010001111110000100011111001100010010101011011100110011110111111011101000110010000011100101110110101111001110000000110100101101010110100100100000100010010110100101101111001100001110010110011111110000000100000001000011111111110010000011010000001011111011101010100110100101000000010111010010011011110111100111001001110110110111100Table 13
Relational vectors.
12345678910111213141516171819200111011100010010000001100000100010011100000001001000010010000110100100000000010010111000100011011001001000011010000001111001001001011000100001101000000100100101100001100010011010000001000100010110011011011110000000010100000000101110000001000100010100000100001001001010110010100001000000000010010011000010110011000110010010011001100011110011001000000000001001101101100010000001000100100100001011011100100000101000001000100110100001101101100010000110100110001101Based on Table13 and definitions in Section 2.2, we could compute the binary norm for each sampling batch Sj (or J) as shown in Table 14.Table 14
Binary norm for the 20 samplings: S1 to S20.
12345678910111213141516171819208111581189614566915178111778


## 6.1. Probability Distribution

We have already constructed the theoretical setting of probability distribution for our testing in Section2.3. Based on that framework and the data given, we could create the theoretical probability distribution prob in Figure 1.Figure 1
Theoretical distribution of binary norm.The (one-tailed) critical values for 5 and 10 percentages are 138 and 78 (via numerical computation), respectively; that is, if the sampled value is larger than the critical values, we should rejectHo: there is no significant relation between the economic freedom and death of COVID-19.


## 6.2. Real Results

In comparison with the absolute reference, we could generate the binary sign vectors for the real data from each samplingSj (or simply j) in Table 12—for the formula and explanation of sign vectors, one could refer to Section 2.2. However, in these 0 and 1 representations, it separates the proportional and inversely proportional relation between the economic freedom and death of COVID-19. To take all the factors into consideration, one further analyses the alternative behaviour of 0 and 1. If there are too many alternations between 0 and 1, it would indicate that there is a less relation between those two. On the other hand, if the alternative times are few, then it leads to the longer length of subvector consisting of pure 1. The alternative results are shown in Table 13.Table 12
Sign vectors.
1234567891011121314151617181920111010011111011110100110000100011010010111111110011011000110000001010001011100011001001111101000101011010100100110101100000010101100010101000110011101100010001111110000100011111001100010010101011011100110011110111111011101000110010000011100101110110101111001110000000110100101101010110100100100000100010010110100101101111001100001110010110011111110000000100000001000011111111110010000011010000001011111011101010100110100101000000010111010010011011110111100111001001110110110111100Table 13
Relational vectors.
12345678910111213141516171819200111011100010010000001100000100010011100000001001000010010000110100100000000010010111000100011011001001000011010000001111001001001011000100001101000000100100101100001100010011010000001000100010110011011011110000000010100000000101110000001000100010100000100001001001010110010100001000000000010010011000010110011000110010010011001100011110011001000000000001001101101100010000001000100100100001011011100100000101000001000100110100001101101100010000110100110001101Based on Table13 and definitions in Section 2.2, we could compute the binary norm for each sampling batch Sj (or J) as shown in Table 14.Table 14
Binary norm for the 20 samplings: S1 to S20.
12345678910111213141516171819208111581189614566915178111778


## 7. Conclusion and Future Work

The contribution of death in COVID-19 is very complicated. We use economic freedom to capture a potential factor in such contribution. To verify the truth of great impact from economic freedom, we devise a metric, two norms, absolute ordering, binary ordering, and probability distribution for the statistical testing population. Based on our research, we find out that the economic freedom has no significant relation to the death of COVID-19. This might provide some reference for the decision makers of the countries. In the future research, one could further study the relation between economic freedom and other ratios related to COVID-19. One could also use other nonparametric approaches to enrich the statistical testing. There is another related paper on the same topic [8]. In that paper, the authors use two-step estimators: negative binomial regression and nonlinear least squares, and find out there is a close relation between economic freedom and fatalities of COVID-19. In essence, their approach focuses more on statistical techniques, while ours focuses more on mathematical approaches. For the future researcher, he could compare or combine these methods to yield a comprehensive or generalised theory that could accommodate and single out the factors that cause the discrepancies.



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*Source: 6660160-2020-12-12.xml*