# Statistical Analysis of COVID-19 Data for Three Different Regions in the Kingdom of Saudi Arabia: Using a New Two-Parameter Statistical Model

Authors: Ibrahim Al-Dayel; Mohammed N. Alshahrani; Ibrahim Elbatal; Naif Alotaibi; A. W. Shawki; Mohammed Elgarhy
Journal: Computational and Mathematical Methods in Medicine
 (2022)

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## Abstract

Since December 2019, the COVID-19 outbreak has touched every area of everyday life and caused immense destruction to the planet. More than 150 nations have been affected by the coronavirus outbreak. Many academics have attempted to create a statistical model that may be used to interpret the COVID-19 data. This article extends to probability theory by developing a unique two-parameter statistical distribution called the half-logistic inverse moment exponential (HLIMExp). Advanced mathematical characterizations of the suggested distribution have explicit formulations. The maximum likelihood estimation approach is used to provide estimates for unknown model parameters. A complete simulation study is carried out to evaluate the performance of these estimations. Three separate sets of COVID-19 data from Al Bahah, Al Madinah Al Munawarah, and Riyadh are utilized to test the HLIMExp model’s applicability. The HLIMExp model is compared to several other well-known distributions. Using several analytical criteria, the results show that the HLIMExp distribution produces promising outcomes in terms of flexibility.


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## Body

## 1. Introduction

In recent years, many various of statisticians have been attracted by create new families of distributions for example; exponentiated generalized-G in [1], logarithmic-X family of distributions [2], sine-G in [3], odd Perks-G in [4], odd Lindley-G in [5], truncated Cauchy power-G in [6], truncated Cauchy power Weibull-G-G in [7], Topp-Leone-G in [8], odd Nadarajah–Haghighi-G in [9], the Marshall–Olkin alpha power-G in [10], T-X generator studied in [11], type I half-logistic Burr X-G in [12], KM transformation family in [13], (DUS) transformation family in [14], arcsine exponentiated-X family in [15], Marshall-Olkin odd Burr III-G family in [16], among others.Reference [17] investigates the half-logistic-G (HL-G) family, a novel family of continuous distributions with an additional shape parameter θ>0. The HL-G cumulative distribution function (cdf) is supplied via
(1)Fz;θ,ω=1−1−Gz;ωθ1+1−Gz;ωθ,z∈R,θ>0.The HL-G family’s density function (pdf) is described as(2)fz;θ,ω=2θgz;ω1−Gz;ωθ−11+1−Gz;ωθ2,z∈R,θ>0,respectively. A random variable (R.v)Zhas pdf (2) which would be specified asZ~HL−Gz;ω.Reference [18] presented the moment exponential (MExp) model by allocating weight to the exponential (Exp) model. They established that the MExp distribution is more adaptable than the Exp model. The cdf and pdf files are available.
(3)Gt;β=1−1+tβe−t/β,t>0,(4)gt,β=tβ2e−t/β,t>0,respectively, where β>0 is a scale parameter.The inverse MExp (IMExp) distribution was presented in reference [19], and it is produced by utilizing the R.v Z=1/T, where T is as follows (4). The cdf and pdf files in the IMExp distribution are specified as
(5)Gz;β=1+βze−β/z,z>0,β>0,gz;β=β2z3e−β/z,z>0,β>0.In this research, we propose an extension of the IMExp model, which is built using the HL-G family and the IMExp model, known as the half-logistic inverse moment exponential (HLIMExp) distribution.The aim goal of this article can be considered in the following items:(i)
To introduce a new two-parameter lifetime model which is called the HLIMExp(ii)
The new model is very flexible, and the pdf can take different shapes such as unimodal, right skewness, and heavy tail. Also, the hrf can be increasing, upside-down, and J-shaped(iii)
Many numerical values of the moments are calculated in Table1. And we can note from it that (a) whenβ=3andθis increasing, then the numerical values ofEZ,EZ2,EZ3,EZ4, varianceσ2, skewness (SK), and kurtosis (KU) are decreasing but the numerical values of harmonic mean (H) are increasing(iv)
The simulation study is carried out to assess the behavior of parameters, and the numerical results are mentioned in Tables2–5. From these tables, we can note that when the value of n is increased, the value of Ω1 and Ω4 is decreased(v)
Three separate sets of COVID-19 data from Al Bahah, Al Madinah Al Munawarah, and Riyadh are utilized to test the HLIMExp model’s applicability. The HLIMExp model is compared to several other well-known distributions. Using several analytical criteria, the results show that the HLIMExp distribution produces promising outcomes in terms of flexibilityTable 1
Numerical values of Mos for the HLIMExp model forβ=3 different values of parameter 𝜃.
θEZEZ2EZ3EZ4Hσ2SKKUCV40.4529.9511.7020.2901.0066.5822.9921.7091.1924.50.4258.3351.5130.2271.0524.4692.3411.4861.12250.4047.2931.3700.1861.0923.2751.9151.3221.0665.50.3876.5681.2560.1561.1302.5311.6161.1971.02060.3726.0361.1630.1341.1642.0341.3981.0980.9826.50.3605.6301.0860.1171.1951.6841.2311.0180.94970.3495.3101.0190.1031.2241.4271.1010.9520.9217.50.3405.0520.9610.0931.2511.2320.9960.8960.89680.3314.8400.9100.0841.2761.0800.9100.8480.8748.50.3244.6620.8650.0771.3000.9590.8390.8070.855Table 2
MLEs,Ω1s, Ω2, Ω3, and Ω4 of the HLIMExp model for β=0.5 and θ=0.5.
nMLEsΩ190%95%Ω2Ω3Ω4Ω2Ω3Ω4300.5820.0420.3600.8050.4450.3170.8470.5300.5710.0370.3090.8330.5230.2590.8830.624500.5480.0090.3810.7150.3340.3490.7470.3980.5930.0250.3660.8190.4530.3230.8620.5391000.5500.0050.4190.6800.2610.3940.7050.3110.5280.0090.3730.6840.3110.3430.7140.3713000.5110.0030.4260.5960.1700.4100.6120.2020.4960.0050.3910.6010.2110.3710.6210.2514000.5100.0010.4610.5590.0980.4520.5680.1160.5250.0030.4600.5890.1290.4480.6020.1545000.5110.0010.4730.5480.0760.4650.5560.0900.5220.0020.4720.5710.0990.4620.5810.119Table 3
MLEs,Ω1s, Ω2, Ω3, and Ω4 of HLIMExp model for β=0.5 and θ=0.8.
nMLEsΩ190%95%Ω2Ω3Ω4Ω2Ω3Ω4300.5040.0140.3170.6910.3740.2810.7270.4460.9550.1940.4601.4500.9900.3651.5451.179500.5230.0130.3650.6820.3160.3350.7120.3770.9550.0630.5621.3480.7860.4871.4230.9361000.5240.0060.4010.6470.2450.3780.6700.2920.8640.0210.5921.1370.5450.5401.1890.6493000.5120.0030.4280.5970.1690.4110.6130.2020.8400.0110.6521.0280.3760.6151.0640.4484000.5040.0010.4560.5520.0960.4470.5610.1140.7940.0030.6910.8970.2050.6720.9160.2455000.5030.0000.4660.5400.0740.4590.5470.0880.8140.0030.7320.8960.1630.7170.9110.195Table 4
MLEs,Ω1s, Ω2, Ω3, and Ω4 of HLIMExp model for β=0.5 and θ=1.2.
nMLEsΩ190%95%Ω2Ω3Ω4Ω2Ω3Ω4300.5190.0060.3550.6830.3290.3230.7150.3921.5190.3370.7422.2951.5540.5932.4441.851500.4880.0070.3700.6070.2370.3470.6290.2821.1220.0330.6831.5620.8790.5991.6461.0471000.5070.0050.4200.5950.1750.4030.6120.2091.2400.0830.9001.5790.6790.8351.6440.8093000.5080.0010.4460.5700.1240.4340.5820.1481.2440.0321.0021.4850.4840.9551.5320.5764000.5020.0010.4520.5510.1000.4420.5610.1191.2070.0111.0161.3990.3840.9791.4360.4575000.4910.0010.4490.5330.0840.4410.5420.1011.1760.0111.0141.3390.3250.9821.3700.388Table 5
MLEs,Ω1s, Ω2, Ω3, and Ω4 of HLIMExp model for β=1.5 and θ=1.2.
nMLEsΩ190%95%Ω2Ω3Ω4Ω2Ω3Ω4301.6870.2771.0102.3631.3530.8812.4921.6121.2390.0430.8531.6260.7730.7791.7000.921501.5260.0451.0701.9820.9120.9832.0701.0871.2250.0140.9091.5010.5920.8521.5570.7061001.5290.0321.2061.8520.6461.1441.9140.7701.2180.0120.9991.4180.4190.9591.4580.4993001.5560.0141.3661.7470.3811.3301.7830.4541.2150.0061.1211.3690.2491.0971.3930.2974001.5130.0051.3541.6720.3181.3231.7020.3791.1980.0031.0941.3020.2081.0741.3210.2485001.5450.0111.3991.6910.2921.3721.7190.3481.2010.0011.1311.3210.1891.1131.3390.225The following is an outline of the remainder of this article: Section2 discusses the construction of the HLIMExp model. Section 3 calculates the basic properties of the distribution, including the linear representation of HLIMExp pdf, order statistics, moments, moment generating function, and conditional moment. In contrast, Section 4 discusses parameter estimation using the maximum likelihood (ML) estimation method. Section 5 employs Monte Carlo simulation techniques. In Section 6, we investigated the potentiality of the HLIMExp using three different metrics of goodness of fit such as the Akaike Information Criterion (IC) (V1), Consistent AIC (V2), Bayesian IC (V3), Hannan-Quinn IC (V4), Kolmogorov–Smirnov (V5) test, and p value (V6). Finally, Section 7 mentions the conclusion.


## 2. The New Two-Parameter Statistical Model

A nonnegative R.vZ with the HLIMExp model is constructed by putting (5) and (6) in (1) and (2), respectively; we should get cdf and pdf.
(6)Fz;β,θ=1−1−1+β/ze−β/zθ1+1−1+β/ze−β/zθ,z>0,β,θ>0.(7)fz;β,θ=2θβ2/z3e−β/z1−1+β/ze−β/zθ−11+1−1+β/ze−β/zθ2,z>0,θ>0.The survival function (sf) is provided by(8)F¯z;β,θ=21−1+β/ze−β/zθ1+1−1+β/ze−β/zθ,z>0,β,θ>0.The hrf or failure rate and reversed hrf for the HLIMExp are calculated as follows:(9)hz;β,θ=θβ2/z3e−β/z1−1+β/ze−β/z1+1−1+β/ze−β/zθ,τz;β,θ=2θβ2/z3e−β/z1−1+β/ze−β/zθ−11−1−1+β/ze−β/z2θ.Different shapes of the pdf and hrf of HLIMExp with different parameter values are mentioned in Figures1 and 2.Figure 1
Different shapes of pdf for the HLIMExp model.Figure 2
Different shapes of hrf for the HLIMExp model.


## 3. Statistical Properties

We discussed certain HLIMExp distribution features in this part, including linear representation of HLIMExp pdf, moments (Mo), the harmonic mean (H), moment generating function (MoGF), and conditional moment (CoMo).


### 3.1. Linear Representation

A linear form of the pdf and cdf is offered in this part to introduce statistical properties of the HLIMExp distribution. Using the following binomial expansion,(10)1+z−m=∑i=0∞−1im+i−1izi,where∣z∣<1 and b is a positive real noninteger. By applying (10) in the next term, we get
(11)1+1−1+βze−β/zθ−2=∑i=0∞−1ii+11−1+βze−β/zθi.Inserting the previous equation in (7), we have
(12)fz;β,θ=2θβ2∑i=0∞−1ii+1z−3e−β/z1−1+βze−β/zθi+1−1.Again, applying the general binomial theorem, we get(13)1−1+βze−β/zθi+1−1=∑j=0∞−1jθi+1−1j1+βzje−jβ/z.Inserting the previous equation in (7), we have
(14)fz;β,θ=2θβ2∑i,j=0∞−1i+ji+1θi+1−1jz−3e−βj+1/z1+βzj.Again, using the binomial expansion, we get
(15)fz;β,θ=∑k=0∞Skz−k−3e−βj+1/z,where
(16)Sk=2θβk+2∑i,j=0∞−1i+ji+1jkθi+1−1j.


### 3.2. Moments

Therth Mos of the HLIMExp distribution are discussed in this subsection. Moments are essential in any statistical study, but especially in applications, it can be used to investigate the main properties and qualities of a distribution (e.g., tendency, dispersion, skewness, and kurtosis). The rth Mo of Z denoted by μ`r may be calculated using (8).
(17)μ`r=EZr=∑k=0∞Sk∫0∞zr−k−3e−βj+1/zdz,then,
(18)μ`r=∑k=0∞Skβj+1−r−k−2Γk+r+2.Therth inverse Mo of Z denoted by μ`r may be calculated using (8).
(19)μ`r−1=EZ−r=∑k=0∞Sk∫0∞zr−k−3e−βj+1/zdz,then,
(20)μ`r−1=∑k=0∞Skβj+1r−k−2Γk−r+2.The harmonic mean ofZ is given by
(21)H=E1Z=∑k=0∞Sk∫0∞z−k−4e−βj+1/zdz,then,
(22)μ`r=∑k=0∞Skβj+1−k−3Γr+3.MoGFs are useful for several reasons, one of which is their application to analysis of sums of random variables. The MoGF ofZMzt is deduced from (7) as
(23)Mzt=∑r=0∞trr!μr′=∑r=0∞∑k=0∞SktrΓk−r+2βj+1r−k−2r!.Numerical values for specific values of parameters of the first four ordinary Mos,EZ, EZ2, EZ3, EZ4, variance σ2, skewness (SK), and kurtosis (KU) of the HLIMExp model are reported in Table 1.


### 3.3. The Conditional Moment

For empirical intents, the shapes of various distributions, such as income quantiles and Lorenz and Bonferroni curves, can be usefully described by the first incomplete moment, which plays a major role in evaluating inequality. These curves have a variety of applications in economics, reliability, demographics, insurance, and medical. LetZ denote a R.v with the pdf given in (7). The sth upper incomplete Mo say ηst could be expressed with
(24)ηst=∫t∞zsfz;β,θdz=∑k=0∞Sk∫t∞zs−k−3e−βj+1/zdz=∑k=0∞Skβj+1s−k−2Γk−s+2,βj+1t.Similarly, thesth lower incomplete Mo function is provided through
(25)ϕst=∫0tzsfz;β,θdz=∑k=0∞Sk∫0tzs−k−3e−βj+1/zdz=∑k=0∞Skβj+1s−k−2γk−s+2,βj+1t.


## 3.1. Linear Representation

A linear form of the pdf and cdf is offered in this part to introduce statistical properties of the HLIMExp distribution. Using the following binomial expansion,(10)1+z−m=∑i=0∞−1im+i−1izi,where∣z∣<1 and b is a positive real noninteger. By applying (10) in the next term, we get
(11)1+1−1+βze−β/zθ−2=∑i=0∞−1ii+11−1+βze−β/zθi.Inserting the previous equation in (7), we have
(12)fz;β,θ=2θβ2∑i=0∞−1ii+1z−3e−β/z1−1+βze−β/zθi+1−1.Again, applying the general binomial theorem, we get(13)1−1+βze−β/zθi+1−1=∑j=0∞−1jθi+1−1j1+βzje−jβ/z.Inserting the previous equation in (7), we have
(14)fz;β,θ=2θβ2∑i,j=0∞−1i+ji+1θi+1−1jz−3e−βj+1/z1+βzj.Again, using the binomial expansion, we get
(15)fz;β,θ=∑k=0∞Skz−k−3e−βj+1/z,where
(16)Sk=2θβk+2∑i,j=0∞−1i+ji+1jkθi+1−1j.


## 3.2. Moments

Therth Mos of the HLIMExp distribution are discussed in this subsection. Moments are essential in any statistical study, but especially in applications, it can be used to investigate the main properties and qualities of a distribution (e.g., tendency, dispersion, skewness, and kurtosis). The rth Mo of Z denoted by μ`r may be calculated using (8).
(17)μ`r=EZr=∑k=0∞Sk∫0∞zr−k−3e−βj+1/zdz,then,
(18)μ`r=∑k=0∞Skβj+1−r−k−2Γk+r+2.Therth inverse Mo of Z denoted by μ`r may be calculated using (8).
(19)μ`r−1=EZ−r=∑k=0∞Sk∫0∞zr−k−3e−βj+1/zdz,then,
(20)μ`r−1=∑k=0∞Skβj+1r−k−2Γk−r+2.The harmonic mean ofZ is given by
(21)H=E1Z=∑k=0∞Sk∫0∞z−k−4e−βj+1/zdz,then,
(22)μ`r=∑k=0∞Skβj+1−k−3Γr+3.MoGFs are useful for several reasons, one of which is their application to analysis of sums of random variables. The MoGF ofZMzt is deduced from (7) as
(23)Mzt=∑r=0∞trr!μr′=∑r=0∞∑k=0∞SktrΓk−r+2βj+1r−k−2r!.Numerical values for specific values of parameters of the first four ordinary Mos,EZ, EZ2, EZ3, EZ4, variance σ2, skewness (SK), and kurtosis (KU) of the HLIMExp model are reported in Table 1.


## 3.3. The Conditional Moment

For empirical intents, the shapes of various distributions, such as income quantiles and Lorenz and Bonferroni curves, can be usefully described by the first incomplete moment, which plays a major role in evaluating inequality. These curves have a variety of applications in economics, reliability, demographics, insurance, and medical. LetZ denote a R.v with the pdf given in (7). The sth upper incomplete Mo say ηst could be expressed with
(24)ηst=∫t∞zsfz;β,θdz=∑k=0∞Sk∫t∞zs−k−3e−βj+1/zdz=∑k=0∞Skβj+1s−k−2Γk−s+2,βj+1t.Similarly, thesth lower incomplete Mo function is provided through
(25)ϕst=∫0tzsfz;β,θdz=∑k=0∞Sk∫0tzs−k−3e−βj+1/zdz=∑k=0∞Skβj+1s−k−2γk−s+2,βj+1t.


## 4. Method of Maximum Likelihood

Letz1,z2,⋯,zn be a random sample of size n from the HLIMExp model with two parameters β and θ; the log-likelihood function is
(26)L=nln2θ−2nlnβ−3∑i=1nzi−∑i=1nβzi+θ−1∑i=1nlogGi−2∑i=1nlog1+Giθ.For calculation MLE estimation, we need partial derivatives ofLZ∣β,θ by parameters
(27)∂logL∂β=−2nβ−∑i=1n1zi++θ−1∑i=1nViGi−2∑i=1nθViGiθ−11+Giθ,∂logL∂θ=nθ+∑i=1nlogGi−2∑i=1nGiθlnGi1+Giθ,where Gi=1−1+β/zie−β/zi and Vi=∂Gi/∂β=β/zi2e−β/zi. As result, estimations of the parameters can be found β^MLE and θ^MLE the solution of the two equations ∂L/∂β=0 and ∂L/∂θ=0 by using software Mathematica (9).


## 5. Simulation Results

A simulation result is included in this section to analyze the behavior of estimators in the presence of complete samples by using the Newton-Raphson iteration method and by using Mathematica (8) software. Mean square errors (Ω1), lower and upper bound (Ω2and Ω3) of confidence interval (CIn), and average length (Ω4) of 90% and 95% are computed using Mathematica 9. The accompanying algorithm is constructed in the next part:
(i)
5000 RS of sizen=30, 50, 100, 300, 400, and 500 are generated from the HLIMExp model(ii)
The parameters’ exact values are chosen(iii)
The ML estimates (MLEs),Ω1s, Ω2, Ω3, and Ω4 for selected values of parameters are computed(iv)
Tables2–5 provide the numerical outputs based on the entire data set


## 6. Applications

This section concerned with three important real data sets. The data called Saudi Arabia Coronavirus cases (COVID-19) situation in Al Bahah, Al Madinah Al Munawarah and Riyadh regions from January 2022 to May 2022.The three data sets were obtained from the following electronic address:https://datasource.kapsarc.org/explore/dataset/saudi-arabia-coronavirus-disease-COVID-19-situation/. The data sets are reported in Table 6. The descriptive analysis of the three data sets is reported in Table 7.Table 6
Al Bahah, Al Madinah Al Munawarah, and Riyadh Regions, coronavirus cases (COVID-19).
YearMonthCoronavirus cases by regionsAl BahahAl Madinah Al MunawarahRiyadh2021Jan8528119942021Feb21327345242021Mar7847556122021Apr2271001120382021May4092266104582021Jun541216775932021Jul772186087472021Aug292105038562021Sep321937602021Oct7895492021Nov6734012021Dec5534125412022Jan14308607441692022Feb6442477196412022Mar7746016122022Apr494236912022May22163170Table 7
Some descriptive analysis of the data.
Al BahahAl Madinah Al MunawarahRiyadhN171717Mean290.5291305.8247373.882Median854603856Skewness1.9823.1082.756Kurtosis4.32710.9278.65Range1424853443999Min673170Max1430860744169Sum493922199125356Here, in this section, the three data sets mentioned below are examined to demonstrate how the HLIMExp distribution outperforms alternative models, comparing the new model to some models, namely, type II Topp-Leone inverse Rayleigh (TIITOLIR) distribution by [20], half-logistic inverse Rayleigh (HLOIR) distribution by [21], beta transmuted Lindley (BTLi) distribution by [22], the transmuted modified Weibull (TMW) distribution by [23], and the weighted Lindley (W-Li) distribution by [24]. We calculate the model parameters’ MLEs and standard errors (SEs). To evaluate distribution models, we use criteria such as the V1, V2, V3, V4, V5, and V6tests. In contrast, the wider distribution relates to smaller V1, V2, V3, V4, and V5 and the highest value of V6. The MLEs of the eight fitted models and their SEs and the numerical values of V1, V2, V3, V4, V5, and V6 for the three data sets are presented in Tables 8–10. We find that the HLIMExp distribution with two parameters provides a better fit than seven models. It has the smallest values of V1, V2, V3, V4, and V5 and the greatest value of V6 among those considered here. Moreover, the plots of empirical cdf, empirical pdf, and PP plots of our competitive model for the three data sets are displayed in Figures 3–5, respectively. The HLIMExp model clearly gives the best overall fit and so may be picked as the most appropriate model for explaining data.Table 8
Numerical values of MLEs, SEs,V1, V2, V3, V4, V5, and V6tests for the first data set.
DistributionsMLE and SEV1V2V3V4V5V6αβθλHLIMExp24.2140.336231.459232.317229.92231.6250.1670.732(9.688)(0.081)TIITOLIR6.6260.196236.208237.065234.669236.3730.2440.265(1.828)(0.051)HLOIR8.7390.272233.253234.11231.714233.4190.2040.48(2.643)(0.059)W-Li0.0880.004232.468233.326230.929232.6340.2750.153(0.078)(0.001)BT-Li0.0100.3200.3590.383232.376235.709229.297232.7070.1810.631(0.017)(0.568)(0.138)(1.139)TMW0.2300.000000010.00270.481235.812241.267231.965236.2260.2430.27(0.140)(0.00002)(0.0011)(0.496)ILBE70.429263.621263.888262.851263.7040.4270.004109(12.078)LBE145.265247.564247.831246.794247.6470.3210.06(24.913)Table 9
Numerical values of MLEs, SEs,V1, V2, V3, V4, V5, and V6tests for the second data set.
DistributionsMLE and SEV1V2V3V4V5V6αβθλHLIMExp292.5610.520276.46277.317274.921276.6260.1180.972(103.158)(0.138)TIITOLIR89.9060.311278.671279.528277.132278.8370.1630.755(20.808)(0.085)HLOIR114.8900.412277.112277.969275.573277.2780.1250.954(29.837)(0.095)W-Li0.0530.0008282.778283.635281.239282.9430.2880.119(0.075)(0.0002)BT-Li0.0010.4960.4780.663284.572287.905281.494284.9030.3580.026(0.002)(0.726)(0.225)(1.037)TMW0.5190.000000040.00060.669286.033291.488282.185286.4470.2390.286(0.400)(0.00002)(0.0002)(0.376)ILBE596.909284.757285.023283.987284.840.2910.112(102.369)LBE652.912294.272294.539293.503294.3550.2720.16(111.973)Table 10
Numerical values of MLEs, SEs,V1, V2, V3, V4, V5, and V6tests for the third data set.
DistributionsMLE and SEV1V2V3V4V5V6αβθλHLIMExp822.8930.377339.578340.435338.039339.7440.1580.788(320.841)(0.093)TIITOLIR224.2040.218344.149345.006342.61344.3140.2160.407(59.549)(0.058)HLOIR292.1580.299341.443342.3339.904341.6090.1780.653(84.846)(0.065)W-Li0.0200.0001341.224342.082339.685341.390.20.506(0.041)(0.00003)BT-Li0.000320.8591.1570.229365.36368.694362.282365.6920.3190.064(0.00007)(0.103)(0.337)(0.385)TMW0.3020.000000270.00010.619345.244350.698341.396345.6580.1790.648(0.177)(0.00008)(0.00004)(0.425)ILBE2175363.338363.605362.569363.4210.4190.0051(372.994)LBE3687356.487356.753355.717356.5690.2810.1360(632.305)Figure 3
The fitted cdf, pdf, and pp plots and fitted sf of the HLIMExp model for the first data.Figure 4
The fitted cdf, pdf, and pp plots and fitted sf of the HLIMExp model for the second data.Figure 5
The fitted cdf, pdf, and pp plots and fitted sf of the HLIMExp model for the third data.


## 7. Conclusion

We propose a novel two-parameter distribution called the half-logistic inverted moment exponential distribution in this research. HLIMExp’s pdf may be written as a linear combination of IMExp densities. We compute explicit formulas for several of its statistical features, such as HLIMExp pdf linear representation, OS, Moms, MoGF, and CoMo. The greatest likelihood estimate is investigated. The accuracy and performance of estimations are evaluated using simulation results. Three separate sets of COVID-19 data from Al Bahah, Al Madinah Al Munawarah, and Riyadh are utilized to test the HLIMExp model’s applicability. The HLIMExp model is compared to several other well-known distributions. Using several analytical criteria, the results show that the HLIMExp distribution produces promising outcomes in terms of flexibility. In the future works, we can use the new suggested model in many works such as (a) using it to study the statistical inference of the suggested model under different censored schemes, (b) using it to study the statistical inference of the suggested model under different ranked set sampling, (c) accelerated lifetime test can be studied for the new model, and (d) the statistical inference of stress strength model for the new suggested model can be studied.



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*Source: 2066787-2022-07-09.xml*