bluuebunny/crossref_metadata_2025 huggingface dataset:
Premium Rates Under Inflationary Conditions
Authors: Waters H.R.
Published: July 2016

This short note has as its starting point an interesting article by Taylor (1979) in which he considered the effects of inflation on a risk process. Taylor showed that if the premium density increased at the same rate as the cost of individual claims then, under certain conditions, ultimate ruin was certain. This raises a natural question, viz. “If the cost of individual claims is increasing how should the premiums be increased in order to keep the probability of ruin under control ?” It is this question that we shall be considering in this note.

In the next section we define the risk process that we shall be studying for the remainder of this note. Our process is essentially a compound Poisson process except that we allow the distribution function of an individual claim to depend on the time at which the claim occurs. We start the third section by deriving, with the help of a general result of Gerber (1973), a formula for the future premium density that will keep the probability of ruin for our process below a predetermined bound. We then derive a simple approximation to this formula that shows more clearly how we require the premium density to change in relation to the change in claims costs. Finally we show that if we consider the same process with annual premiums then the probability of ultimate ruin will be kept below a predetermined bound if the annual premium is calculated according to the principle of zero utility with an exponential utility function or, as a first approximation, according to the variance principle.
The Performance of Alternative Models for Forecasting Automobile Insurance Paid Claim Costs
Authors: Cummins J. David , Powell Alwyn
Published: July 2016

When setting or modifying insurance rates on the basis of observed data, adjustments should be made for inflation between the average claim date of the observation period and the average claim date covered by policies to which the new rates will apply. In automobile insurance ratemaking in the United States, the adjustment is made as follows:

where Lα = trended losses and loss adjustment expenses incurred,

L0 = observed losses and loss adjustment expenses incurred during the experience period,

= the predicted rate of inflation per quarter, and

k = the number of quarters for which losses are being trended.

The inflation coefficient, β, is an exponential growth factor that is estimated using the following equation:

where = average paid claim costs for the year ending in quarter t,

t = time, in quarters, t = 1, 2, …, 12, and

εt = a random disturbance term.

The estimation period for the equation is the twelve quarters immediately preceding the first forecast period, and the estimation is conducted utilizing ordinary least squares. Annual averages of claim costs are used as the dependent variable to smooth random and seasonal fluctuations.
Équilibrage d'un marché de réassurance
Authors: Lemaire Jean , Lorea Michel
Published: July 2016

It is demonstrated that the problems of balancing a reinsurance network and finding the maximum flow in a graph are identical. Gale's theorem is applied first in order to prove a conjecture of Sousselier concerning simple first order networks, next to extend those results to any network. The balanced reinsurance scheme can effectively be constructed by means of Ford and Fulkerson's algorithm, as is shown by an example. Finally, we demonstrate that graph theory provides tools able to tackle more general problems than the one considered by Sousselier: capacity constraints and reinsurance costs are introduced in the model.
Variation de la prime d'assurance de l'assistance pharmaceutique en fonction de la participation de l'assure au coût de l'assistance
Authors: Cannella Salvatore
Published: July 2016

Un nouvel examen des normes qui régissent l'octroi des prestations d'assistance pharmaceutique semble s'imposer. En effet, l'introduction continuelle sur le marché de nouveaux produits pharmaceutiques — dont certains sont capables de juguler rapidement des formes morbides naguère lentes à guérir — et la confiance progressivement accrue que met le grand public dans des ordonnances toujours plus variées exigent, de la part des Instituts d'assurance sociale contre les maladies, des solutions permettant de répondre en même temps à des nécessités diverses: il s'agit en particulier de pouvoir autoriser l'utilisation des produits pharmaceutiques les plus modernes, capables d'accélérer la guérison des malades, même s'ils sont très coûteux, tout en évitant par ailleurs l'expansion anormale des ordonnances et en maintenant le coût de l'assistance dans les limites permises par les possibilités de financement.

Le choix de la solution la meilleure est done subordonné à un ensemble de considérations sur la nécessité et la possibilité des mesures à envisager; les aspects économiques de la question ne sont pas des moindres et leur étude doit de toute évidence reposer sur des bases techniques appropriées.

Il semblerait normal que ces bases techniques soient établies d'après des observations effectuées là où ces mêmes bases techniques doivent être employées; ceci n'est généralement pas possible et c'est pourquoi des éléments provenant d'autres expériences revêtent une importance particulière, ne serait-ce qu'à titre indicatif.
Optimum Structure of Trends of Activities to prevent Chance Damages
Authors: Banasinski Antoni
Published: July 2016

In the socialist countries, where insurance — like the other primary sectors of the national economy — has been nationalized and is conducted by a single state-owned insurance company, a whole number of actuarial problems have arisen. These are problems which either did not interest the private insurance companies or else were marginal questions for them, of no great practical importance. The actuarial problems which have cropped up or have acquired particular importance in the conditions of socialist economy, include questions connected with evaluation of the efficiency of outlays for the insurance company's preventive activities intended to restrict the number and scope of chance damages). Henceforth we shall refer to expenditures of this sort as preventive outlays /expenditures/.

One of the initial problems pertaining to the preventive activities of the state insurance monopoly is one which could be called the optimum structure of the trends of activities to prevent chance damages.

We present the problem in the most simple form, formulating it so that it can be solved by generally-known calculus methods employed in linear programming (e.g. the simplex method given by G. B. Danzig in 1951).

Let us assume that in a given period, e.g. in a year, the insurance company allocates a certain sum I for preventive purposes. Realization of these outlays is expected to reduce damage payments made by the insurance company during that period; let us call that decrease Q, the „savings” obtained by the insurance company.
Bonus ou Malus?
Authors: Gürtler Max
Published: July 2016

Il est peu de problèmes, dans l'industrie de l'assurance, dont la solution occasionne autant de difficultés que celui consistant à fixer dans l'assurance Automobile une prime équitable du point de vue technique.

On a tenté, dans plusieurs pays, de s'attaquer à ce problème par le moyen d'un bonus progressif dont bénéficierait le souscripteur n'annonçant pas de sinistre. Cependant, tant les théoriciens que les praticiens sont très partagés sur l'opportunité de cette solution.

Certains mathématiciens et juristes repoussent catégoriquement le système du bonus et qualifient l'idée de la ristourne d'une partie de la prime à l'assuré n'ayant pas eu de sinistre comme étant contraire à la notion même de l'assurance. Lors d'un des derniers congrès internationaux d'actuaires, ce procédé aurait — avec un peu d'exagération — été défini comme suit: Le bonus est, en matière d'assurance, une renonciation organisée de l'assurance. Cette opinion est principalement défendue par certains actuaires franҁais ).

D'autres mathématiciens, cependant, sont d'avis que le bonus est une précieuse disposition permettant, sur la base des sinistres survenus, d'évaluer chaque risque individuel plus rigoureusement que si I'on renonҁait à cette pratique). Et, à leur avis, il est inopportun de ne pas faire usage de cet élément d'information.

2. “Absence de sinistres” et “Nombre de sinistres”

Normalement, les primes d'assurance dépendent d'un certain nombre de facteurs caractéristiques du risque, à l'exclusion cependant des sinistres concernant un contrat particulier.
Estimation of the coefficient of variation of the excess of loss by means of Jensen's inequality for convex functions. The connection with the theory of life times
Authors: Van Klinken J. , Groenenberg C. J.
Published: July 2016

This note deals with a way to determine upper and lower bounds for the coefficient of variation of the total claim costs in a year in excess of a certain limit value. In many a publication attention has been paid to the question of calculating, in addition to the mean of the excess costs, the variance of these costs. In this connection we only mention here the study of Vajda: Minimum Variance Reinsurance, ASTIN-Bulletin, September 1962. It is evident that in studying such problems of “statistics of large claims” the coefficient of variation, defined as the ratio of the standard deviation and the mean, may be a useful tool. If we exclude special “dangerous” claim distributions and also distributions with a very “irregular” tail, it appears possible to derive bounds for this coefficient of variation and to indicate its asymptotic behaviour. Hereby good use can be made of Jensen's inequality for convex functions. Jensen's inequality has frequently been applied to problems in the field of life insurance mathematics, but as far as the authors of this note know, not to the question mentioned here.

Besides, it may have some interest to point out a connection between the question of estimating the excess of total claim costs and the theory of life times. We may translate “the limit value” as “the age already reached” and “the mean of the excess of loss” as “the expectation of life”. The estimation of the coefficient of variation ot the life time now leads to some well-known biometric formulae on life times and at the same time to an interesting observation as regards human life tables.
A Practical Statistical Method of Estimating Claims Liability and Claims Cash Flow
Authors: Clarke T.G. , Harland N.
Published: July 2016

A few years ago Scurfield (JSS 18) indicated a method used inone U.K. non-Life Office for estimating claims liability for the Motor class of business. Since that paper was written a considerable amount of development has taken place and it is now used in the office as an effective continuous method, using computer techniques, for estimating claims liability. It has also been used for projecting expected cash flow for claims arising in the past.

Whilst it is accepted that the method has limitations, it has been found that an automatic method is required especially in the production of financial models in the non-Life field, and its limitations are outweighed by the fact that there are, in our opinion, no easier methods of producing a satisfactory working model.

In the following paper it is the intention to set out briefly the details of the method, then concentrating on the known limitations and the methods so far devised to combat these limitations. In the appendices we have reproduced some computer printout and figures which will provide practical information on the method.

The principle behind the method is that the “Run-off” of claims payments for any “year of claim”, or similar cohort of claims, follows a particular pattern which experience has shown to be reasonably stable. We can thus study the pattern of claims payments at each stage of “run-off”, say each month and thus ascertain the average and range of values that the historic pattern shows (Fig. 1).

Fig. 1.

Period of delay since beginning of claims Period (Years)
Dynamic Model of Insurance Company's Management
Authors: Frisque Andre
Published: July 2016

In this paper, we are interested in a model related to a number of periods of Company's activity.

The Company calculates an amount s which then could be given as a supplementary interest to the shareholders. This calculated amount is taken from the risk reserve. Let us assume the risk reserve = S at the beginning of an operating period. If the Company gives an amount s to the shareholders, then the risk reserve is S — s. (Borch 1972; Seal 1969).

We must determine the best policy of dividends, that is a rule which determines the payments to be made each year to the shareholders of the Company, maximising a definite criterion.

The problem of dividends must be approached in the “dynamic programming manner”. Indeed, the payments of dividends have an effect upon further gains of the Company and its capacity to pay dividends in the future.

The objective of the Company is, for example, maximising the average utility of the dividend payments, which is calculated according to the distribution of claims. (Borch 1964a; Wolff 1966).
A Note On The Multiplicative Ratemaking Model
Authors: Ajne B.
Published: July 2016

The multiplicative ratemaking, model we have in mind is the following one. Within a certain branch of insurance we have, say for simplicity, two tarif arguments U and V. For example, in motor insurance we could think of U and V as being make of car and geographical district respectively. In fire insurance U could be class of construction for buildings and V could relate to fire defense capacities.

The arguments are of a qualitative nature and argument U has r levels, while argument V has k levels. To our disposal we have statistical experience of the business for a certain period of time, consisting of

—risk exposures nij (i = 1 … r, j = 1 … k).

Risk exposure nij thus corresponds to the ith U-level and the jth V-level. It could be e.g. number of policy years or sum insured during the period of observation for objects belonging simultaneously to U-level i and V-level j.

The nijS are known non-random quantities.

—(relative) risk measures pij(i = 1 … r, j = 1 …k).

Risk measure pij could be e.g. claims frequency, i.e. number of Claims divided by number of policy years, or claims cost per policy year or claims cost as a percentage of sum insured. In general pij is thus the observed number or the observed amount of claims belonging simultaneously to U-level i and V-level j, divided by the corresponding risk exposure nij.
Isotonic Optimization in Tariff Construction
Authors: Jewell W.S.
Published: July 2016

The problem of the best fit to set ideal values under general inequality order restrictions is examined for asymmetric, quadratic, absolute, and Chebyshev norms. Special solution procedures are given in terms of network flow algorithms over a network associated with the given isotonic order relations, and the nature of the optimal solutions is characterized for the different norms.

The model is formulated in terms of finding an optimal insurance rate structure over given risk classes for which a desired pattern of tariffs can be specified. The suitability of different norms is considered in the context of corporate profitability, and the relationship to a simple rate relativities model is described.
Note on the Application of Compound Poisson Processes to Sickness and Accident Statistics
Authors: Philipson Carl
Published: July 2016

In order to fix our ideas an illustration of the theory for (a) a general elementary random process, (b) a compound Poisson process and (c) a Polya process shall be given here below following Ove Lundberg (On Random Processes and Their Application to Accident and Sickness Statistics, Inaug. Diss., Uppsala 1940).

Let the continuous parameter t* be measured on an absolute scale from a given point of zero and consider the random function N* (t*) which takes only non-negative and integer values with N* (o) = o. This function constitutes a general elementary random process for which the conditional probability that N* (t*) = n relative to the hypothesis that shall be denoted , while the absolute probability that N* (t) = n i.e. shall be written If quantities of lower order than dt* are neglected, we may write for the conditional probability that N* (t* + dt*) = n + 1 relative to thehyp othesis that N* (t*) = n, i.e. is the intensity function of the process which is assumed to be a continuous function of t* (the condition of existence for the integral over the given interval of t* for every n > m may be substituted for the condition of continuity). The expectations for an arbitrary but fix value of t* of N* (t*) and p* (t*) will be denoted by the corresponding symbol with a bar so that

If is uniformly bounded for all n in the interval o ≤ t* < T*, where T* is an arbitrary but fix value of t*, we have i.a. that
Sur les événements en chaîne et la distribution binomiale négative généralisée
Authors: Campagne Cornelis
Published: July 2016

Dans plusieurs études [1] Ammeter a démontré que la distribution binomiale négative généralisée peut être interprétée de différentes manières, à savoir comme

a. une contagion des probabilités (Pólya-Eggenberger);

b. une distribution de Poisson basée sur des probabilités fondamentales variables;

c. une distribution de Poisson où la probabilité fondamentale de sinistres n'est pas suffisamment connue;

d. une distribution de Poisson par rapport aux événements, où un seul événement peut comporter plusieurs prétentions de sinistres;

e. une distribution de Poisson basée sur une modification de la répartition des montants de sinistres.

On a, en effet, les relations suivantes:

a. la contagion des probabilités

où F(x, P, h, p(z)) représente la probabilité que le sinistre est au plus égal à x dans un intervalle de temps où le sinistre probable est P. x et P y sont exprimés en le sinistre moyen par événement. p(z)dz est la fonction de fréquence du sinistre par événement.

Nous posons est la convolution de p(z) avec p(z), faite r fois, tandis que h est la notation du paramètre qui figure dans la distribution binomiale négative. Si h est égal à ∞ nous obtenons comme fonction de répartition pour le nombre d'événements survenus la distribution de Poisson.
Assurances Automobiles et Revenus Financiers
Authors: Sousselier Jean
Published: July 2016

La question est controversée de savoir si l'on doit tenir compte du revenu des placements — et éventuellement des bénéfices sur réalisations de valeurs — pour apprécier le résultat technique de la branche Automobiles.

Rappelons qu'en France, réglementairement, dans les états B3 qui font apparaître le résultat technique de la catégorie, on tient compte des frais généraux, ce qui est normal, mais non des intérêts.

En réalité, il semble bien qu'il soit difficile de faire abstraction d'un élément non négligeable de profits et pertes qui dérive de l'exercice même de l'industrie de l'Assurance, mais la question demeure de savoir dans quelle mesure il faut en tenir compte.

Nous allons montrer que la question est intimement liée à la conception même que l'on se fait du montant des réserves techniques à inscrire au passif du bilan.

On ne peut avoir une idée saine tant des résultats techniques que des revenus de placements que si la comptabilité est établie par exercice de souscription. C'est l'hypothèse que nous retiendrons dans ce qui va suivre).

Un tel exercice donne lieu à encaissement d'un certain montant de primes, au paiement de commissions et de frais généraux et enfin au paiement de sinistres s'échelonnant dans le temps, au delà de la clôture calendrier de l'exercice.

Pour plus de rigueur même — et l'on peut se référer au mode de raisonnement appliqué en Assurance sur la Vie — il faut considérer séparément les différentes échéances de primes, chacune se comportant comme une sorte d'exercice isolé: ensemble des assurances à échéance du Ier janvier, ensemble des assurances à échéance du 2 janvier, etc… jusqu'à celles à échéance du 31 décembre. (Il est indifférent de raisonner sur un ensemble ou „en valeur probable” selon le principe actuariel classique).
Colloque Astin 1963 de Trieste Rapport introductif sur le 2e thème, parties b et c
Authors: Sousselier Jean
Published: July 2016

Ce sujet n'a pas été traité, peut-être parce qu'il paraît trop simple; pourtant il mérite examen vu son utilité pratique certaine.

Il est impossible de négliger le jeu de la réserve de Risques en Cours dans l'estimation du taux des sinistres c'est-à-dire dans l'ap-préciation de la tarification et de l'équilibre d'une branche d'assurances.

D'autre part, comme le souligne justement la note introductrice aux thèmes proposés établie par le Comité Astin, le problème est moins immédiat qu'il ne paraît:

On considère généralement la réserve de Risques en Cours (l'expression anglaise risques non expirés est peut-être meilleure) comme un simple pourcentage des primes totales: c'est la fraction de primes non acquise à l'exercice mais ceci suppose que le risque est uniformément réparti dans le temps et que les primes correspondent exactement aux risques couverts.

En fait deux conceptions sont possibles:

— méthode rétrospective: on considère le déroulement passé des opérations: schématiquement on prend la différence entre les primes perҁues et les sinistres survenus; ce qui hypothèque l'avenir.

— méthode prospective: on fixe la somme nécessaire pour faire face aux sinistres à venir dans l'intervalle de temps encore couvert par les polices en cours, ceci compte tenu du taux actuel de sinistres et même de son évolution probable dans le futur immédiat.

La méthode prospective est-elle plus correcte? Il peut le sembler. Mais c'est seulement viser à l'équilibre probable du bilan futur, au détriment du bilan actuel. Pourquoi une insuffisance de tarification, par exemple, doit-elle peser sur le seul compte de l'exercice clos?
Reserves in Sanatorium Insurance
Authors: Welten C. P.
Published: July 2016

The object of the Netherlands Foundation for Sanatorium Insurance (“N.S.V.”) is to insure the risk of treatment in a sanatorium because of tuberculosis. For insured persons admitted to a sanatorium because of tuberculosis, the N.S.V. pays the insured sum for every day of treatment. At the moment nearly 80% of the population of the Netherlands is insured directly or indirectly in the N.S.V.

There are three groups of insurances: obligatory insurance, voluntary collective insurances and voluntary individual insurances. The insurances in the first and second group are, strictly speaking, reinsurances of the risk of tuberculosis of a great number of institutions concerned with cost of sickness insurance. The risk of the insurance in these two groups is only administered and pooled by the N.S.V.

This paper concerns the group of the individual insurances only, which group contains about 1.250.000 insured persons. The risk of this group is run by the N.S.V. itself. As the N.S.V. is a non-profit organisation, the premium level is held as low as possible.

From statistical data, derived from the administration of the N.S.V., the “admission frequency” is calculated every year, being the quotient of the number of insured persons, admitted to a sanatorium in that year, and the total number of insured persons. This admission frequency a, which is now about is used as a basis for the calculation of the premium which will be in force during the next year.
On the Calculation of the Generalised Poisson Function
Authors: Pesonen Erkki
Published: July 2016

Drs. H. Bohman and F. Esscher have reported in a recent paper) an extensive research performed in Sweden on the different methods of calculation of the distribution function of the total amount of claims. In the present paper certain methods are discussed in so far as they are different from those presented in the above quoted paper. The consideration is restricted to the generalised Poisson function even though some results can be easily extended. The author has already commented on some of the results represented in the sequel at a special meeting of the 17th International Congress of Actuaries in Edinburgh.

I. Lemma. Let be the generalised Poisson function under investigation. If aiSi(x), where Σ ai = 1 (the functions Si need not be distribution functions, neither must the constants ai be real numbers of interval [0,1]), then

F(x; n, S) = F(.; a1n, S1) * …*F(.; arn, Sr) (x),

as is easily verified by the use of characteristic functions. This component representation is repeatedly used in the sequel.

2. A Modified Esscher Method. The Esscher method is based on an observation that the well-known Edgeworth expansion is more advantageously applicable to a conveniently modified distribution function instead of the original generalised Poisson function. Let us assume that the value of F(x) is required at a point
Astin Colloquium at Randers: Subject A Report
Authors: Segerdahl Carl-Otto
Published: July 2016

Our discussions today will concern Subject A: Risk Theory, in particular the overall risk involved in operating an insurance concern. 7 papers have been handed in to the Colloquium on this subject.

To be quite candid, the referee would like to say that only one of these papers really treats the whole of the topic foreseen, and this is the paper by Mr. Colin M. Stewart (U.K.): The Assessment of Solvency. The other papers treat different special practical sides of the problem as well as general risk theoretical questions. One of the papers, that of Mr. Brichler, could have been attributed to Subject B as well as to Subject A, but it has been decided to take it up for treatment today.

Mr. Stewart delivers a lot of interesting points, which, I may say, take into account the solvency aspect as it looks to the supervisory authorities much more than has been done within the ASTIN discussions earlier. This, of course, is very related to the fact that regional as well as Common Market discussions have resulted in or will result in legislative rules for judging the solvency of insurance concerns, which rules will have great practical importance in the future. Mr. Stewart stresses the point that in case of non-life concerns it is the business on the books and its future contracted periods, short time business to be signed before judgment can be practically undertaken, claims reported, claims occurred but not yet reported, as compared with free reserves available that really decide the matter of sovency.
Étude sur la survenance des sinistres en Assurance Automobile
Authors: Brichler M.
Published: July 2016

On sait que la loi de Poisson simple représente mal la distribution des sinistres d'un groupe observé d'automobilistes du fait que tout groupe que l'on peut étudier en pratique, même s'il est composé d'assurés présentant des caractéristiques communes (même zone de circulation, même type de véhicule, même utilisation de ce véhicule, …) est hétérogéne quant aux autres caractéristiques et surtout quant au comportement personnel des assurés, élément dont l'influence sur les résultats du risque est prépondérante.

M. Delaporte a obtenu une représentation intéressante du phénomène en supposant que les sinistres d'un véhicule se répartis-sent suivant une loi de Poisson de moyenne donnée, et que les moyennes de chaque véhicule du groupe étudié se distribuent selon une loi de Pearson type III d'equation:

où Γ(b) est la fonction eulérienne de 21ème espèce:

a, b, et S0 étant des paramètres dont la valeur est calculée en égalant les expressions des 3 premiers moments théoriques aux moments correspondants observés.

Cette formule conduit à des calculs assez longs.

M. Depoid a proposé une formule plus simple.
Les Mathématiques de L'Assurance Automobile
Authors: Delaporte P. J.
Published: July 2016

Plusieurs communications sont présentées au Colloque sur les Mathématiques de l'Assurance Automobile. Afin de pouvoir mieux situer chacune d'elles dans ce vaste sujet, il peut être bon de schématiser l'ensemble de la question. Il comprend:

1. la survenance des accidents

2. le tarif et la mesure de son efficacité par rapport à l'estimation optimale.

Groupons dans une classe les propriétaires de véhicules ayant un même ensemble de caractéristiques extérieures de risques: même modèle de voiture, même zone de garage habituel, même usage ou profession du propriétaire, etc. Les risques s de survenance d'accident ne sont pas identiques pour tous les propriétaires de la classe, mais sont distribués selon une fonction de répartition F(s).

Désignons par P(s′ ∣ s) la probabilité de survenance de s′ sinistres pour un assuré dont le risque individuel est s (des études antérieures ont montré que P(s′ ∣ s) est représentable par une loi de probabilité de Poisson). La probabilité qu'un assuré, pris au hasard dans la classe, ait s′ sinistres est:

s0 étant le risque minimum de la classe.

Désignons par g(X) la densité de probabilité de la distribution des couts X des sinistres. On peut admettre qu'à l'intérieur de la classe, au moins en première approximation, g(X) est indépendant de s, d'où la probabilité de survenance d'un sinistre de coût X est:
The Influence of the franchise on the number of claims in Motor Insurance
Authors: Muff Mogens
Published: July 2016

1. If you introduce a franchise or raise its amount, the number of claims will decrease. One reason why you will operate a franchise in car damage insurance is to avoid the troublesome and expensive handling of the large number of very small claims.

Therefore, the management could use a mathematical model describing the number of claims as related to the size of the franchise. By varying this figure one may find the franchise that provides for the optimal business conditions.

2. The mathematical model to be described in this paper was found by studying the distribution of the claims in two portfolios. The general conditions of the two groups were as equal as possible, there was no-claim bonus in neither group, but group B had a franchise of 250 DKr. (about US $ 35) while group A covered the smaller claims also. Each policy had been unaltered for at least one year. The number of claims during 12 successive months was registered as follows:

The distribution could be described by a negative binomial distribution

where the parameters α and γ were estimated by

These estimates are not maximum likelihood estimates but it was not regarded necessary to improve the estimation as the χ2 values of the incomplete χ2-test were found as

The parameters were estimated as follows:

3. Special interest is attached to the variations of the γ-parameter. It is well known, that if γ → ∞ and α → ∞ under the condition then the negative binomial distribution will converge towards a Poisson distribution with the parameter λ.
Multistage Curve Fitting
Authors: von Lanzenauer Christoph Haehling , Wright Don
Published: July 2016

One of the most important properties of a distribution function is that it fits the data well enough for the decision-makers' or analysts' purposes. The statisticians' problem is to select a specific form for the distribution function and to determine its parameters from the available data. Various methods (graphical method, method of moments, maximum likelihood method) are available for that purpose.

In many real world situations a single distribution function, however, may not be appropriate over the entire range of the available data. This suggests that the underlying process changes over the range of the respective variable. This fact should be considered in curve fitting. A typical example of such a situation is given in Figure 1 representing third party liability losses for trucks.

It is interesting to speculate about the different raisons d'être (Seal [5]) for the observed discontinuity. It may be the result of out-of-court or in-court settlements or could stem from differences between bodily injury and property damages.
On the Calculation of Variances and Credibilities by Experience Rating
Authors: Loimaranta K.
Published: July 2016

By experience rating the main problem is to estimate the credibilities. We have for the credibility αk the famous formula)

but it is often troublesome to find suitable estimates for the variances and . In the present paper a general method to estimate them from the actual statistics is given.

A disadvantage of the method is that good estimates require relatively extensive statistical material. If one of the variances is known, the method can be easily modified to give the other variance from statistics of moderate size.

The method is based on the Maximum Likelihood principle and leads to a system of non-linear equations. The equations can be solved by an iterative process, easily programmable for computers.

The mathematical model underlying the experience rating problem differs in our case lightly from the usual one.
Nonparametric Estimation of the Probability of Ruin
Authors: Frees Edward W.
Published: July 2016

The finite and infinite horizon time probability of ruin are important parameters in the study of actuarial risk theory. This paper introduces procedures for directly estimating these key parameters from a random sample of observations without assumptions as to the parametric form of the distribution from which the observations arise. The estimators introduced apply to most of the classical models in which ruin probabilities are used and also apply to a much broader class of models. The procedures are based on the concept of sample reuse, an old idea in statistics which is becoming more popular due to the widespread availability of high speed computers. In this paper, the almost sure consistency of the estimators is established. Further, finite sample properties of the estimators are investigated in a simulation study.
Dynamics of dental evolution in ornithopod dinosaurs
Authors: Strickson Edward , Prieto-Márquez Albert , Benton Michael J. , Stubbs Thomas L.
Published: July 2016

Ornithopods were key herbivorous dinosaurs in Mesozoic terrestrial ecosystems, with a variety of tooth morphologies. Several clades, especially the ‘duck-billed’ hadrosaurids, became hugely diverse and abundant almost worldwide. Yet their evolutionary dynamics have been disputed, particularly whether they diversified in response to events in plant evolution. Here we focus on their remarkable dietary adaptations, using tooth and jaw characters to examine changes in dental disparity and evolutionary rate. Ornithopods explored different areas of dental morphospace throughout their evolution, showing a long-term expansion. There were four major evolutionary rate increases, the first among basal iguanodontians in the Middle-Late Jurassic and the three others among the Hadrosauridae, above and below the split of their two major clades, in the middle of the Late Cretaceous. These evolutionary bursts do not correspond to times of plant diversification, including the radiation of the flowering plants and suggest that dental innovation rather than coevolution with major plant clades was a major driver in ornithopod evolution.
Dynamic studies of H-Ras•GTPγS interactions with nucleotide exchange factor Sos reveal a transient ternary complex formation in solution
Authors: Vo Uybach , Vajpai Navratna , Embrey Kevin J. , Golovanov Alexander P.
Published: July 2016

The cycling between GDP- and GTP- bound forms of the Ras protein is partly regulated by the binding of Sos. The structural/dynamic behavior of the complex formed between activated Sos and Ras at the point of the functional cycle where the nucleotide exchange is completed has not been described to date. Here we show that solution NMR spectra of H-Ras∙GTPγS mixed with a functional fragment of Sos (SosCat) at a 2:1 ratio are consistent with the formation of a rather dynamic assembly. H-Ras∙GTPγS binding was in fast exchange on the NMR timescale and retained a significant degree of molecular tumbling independent of SosCat, while SosCat also tumbled largely independently of H-Ras. Estimates of apparent molecular weight from both NMR data and SEC-MALS revealed that, at most, only one H-Ras∙GTPγS molecule appears stably bound to Sos. The weak transient interaction between Sos and the second H-Ras∙GTPγS may provide a necessary mechanism for complex dissociation upon the completion of the native GDP → GTP exchange reaction, but also explains measurable GTP → GTP exchange activity of Sos routinely observed in in vitro assays that use fluorescently-labelled analogs of GTP. Overall, the data presents the first dynamic snapshot of Ras functional cycle as controlled by Sos.
CD47 Promotes Tumor Invasion and Metastasis in Non-small Cell Lung Cancer
Authors: Zhao Hui , Wang Jianxin , Kong Xiaodan , Li Encheng , Liu Yuanbin , Du Xiaohui , Kang Zhijie , Tang Ying , Kuang Yanbin , Yang Zhihui , Zhou Youwen , Wang Qi
Published: July 2016

CD47 is overexpressed in many human cancers, its level positively correlates with tumor invasion and metastasis. However, it is largely unknown whether CD47 overexpression drives metastasis and how CD47 lead to tumor metastasis in non-small cell lung cancer (NSCLC). In this study, we analyzed NSCLC specimens and cell lines and revealed that CD47 is expressed at a higher level than in tumor-free control samples. Furthermore, increased CD47 expression correlated with clinical staging, lymph node metastasis and distant metastasis. In order to understand the molecular mechanisms underlying CD47 functions, we applied both gain-of-function and loss-of-function approaches in cell lines. The siRNA-mediated downregulation of CD47 inhibited cell invasion and metastasis in vitro, while the overexpression of CD47 by plasmid transfection generated opposite effects. In vivo, CD47-specific shRNA significantly reduced tumor growth and metastasis. On the molecular level, the expression of CD47 correlated with that of Cdc42, both in cell lines and NSCLC specimens. The inhibition of Cdc42 attenuates the invasion and metastasis of CD47-overexpressing cells. These results indicate that Cdc42 is a downstream mediator of CD47-promoted metastasis. Our findings provide first evidence that CD47 is an adverse prognostic factor for disease progression and metastasis and a promising therapeutic target for NSCLC.
Quantum steering of Gaussian states via non-Gaussian measurements
Authors: Ji Se-Wan , Lee Jaehak , Park Jiyong , Nha Hyunchul
Published: July 2016

Quantum steering—a strong correlation to be verified even when one party or its measuring device is fully untrusted—not only provides a profound insight into quantum physics but also offers a crucial basis for practical applications. For continuous-variable (CV) systems, Gaussian states among others have been extensively studied, however, mostly confined to Gaussian measurements. While the fulfilment of Gaussian criterion is sufficient to detect CV steering, whether it is also necessary for Gaussian states is a question of fundamental importance in many contexts. This critically questions the validity of characterizations established only under Gaussian measurements like the quantification of steering and the monogamy relations. Here, we introduce a formalism based on local uncertainty relations of non-Gaussian measurements, which is shown to manifest quantum steering of some Gaussian states that Gaussian criterion fails to detect. To this aim, we look into Gaussian states of practical relevance, i.e. two-mode squeezed states under a lossy and an amplifying Gaussian channel. Our finding significantly modifies the characteristics of Gaussian-state steering so far established such as monogamy relations and one-way steering under Gaussian measurements, thus opening a new direction for critical studies beyond Gaussian regime.
Pre-hospital delay and its associated factors in first-ever stroke registered in communities from three cities in China
Authors: Jiang Bin , Ru Xiaojuan , Sun Haixin , Liu Hongmei , Sun Dongling , Liu Yunhai , Huang Jiuyi , He Li , Wang Wenzhi
Published: July 2016

This study aimed to explore pre-hospital delay and its associated factors in first-ever stroke registered in communities from three cities in China. The rates of delay greater than or equal to 2 hours were calculated and factors associated with delays were determined by non-conditional binary logistic regression, after adjusting for different explanatory factors. Among the 403 cases of stroke with an accurate documented time of prehospital delay, the median time (interquartile range) was 4.00 (1.50–14.00) hours. Among the 544 cases of stroke with an estimated time range of prehospital delay, 24.8% of patients were transferred to the emergency department or hospital within 2 hours, only 16.9% of patients with stroke were aware that the initial symptom represented a stroke, only 18.8% used the emergency medical service and one-third of the stroke cases were not identified by ambulance doctors. In the multivariate analyses, 8 variables or sub-variables were identified. In conclusion, prehospital delay of stroke was common in communities. Thus, intervention measures in communities should focus on education about the early identification of stroke and appropriate emergency medical service (EMS) use, as well as the development of organized stroke care.
Palladium(ii)-catalyzed C–C and C–O bond formation for the synthesis of C1-benzoyl isoquinolines from isoquinoline N-oxides and nitroalkenes
Authors: Li Jiu-ling , Li Wei-ze , Wang Ying-chun , Ren Qiu , Wang Heng-shan , Pan Ying-ming
Published: July 2016

C1-Benzoyl isoquinolines can be generated via a palladium(ii)-catalyzed C–C and C–O coupling of isoquinoline N-oxides with aromatic nitroalkenes.
Inhibitory effect of MnCr2O4 spinel coating on coke formation during light naphtha thermal cracking
Authors: Bao Binbin , Liu Jinglei , Xu Hong , Liu Bo , Zhang Weifeng
Published: July 2016

MnCr2O4 spinel coating can significantly affect coke morphology and coke microstructure.
Non-precious Mn1.5Co1.5O4–FeNx/C nanocomposite as a synergistic catalyst for oxygen reduction in alkaline media
Authors: Jiang Rongzhong , Tran Dat T. , McClure Joshua P.
Published: July 2016

A nanocomposite material containing non-precious bimetal oxides and FeN-doped carbon was synthesized with double synergistic effect for ORR.
Synthesis, characterization, and thermoelectric properties of superconducting (BEDT-TTF)2I3nanoparticles
Authors: Chtioui-Gay I. , Faulmann C. , de Caro D. , Jacob K. , Valade L. , de Caro P. , Fraxedas J. , Ballesteros B. , Steven E. , Choi E. S. , Lee M. , Benjamin S. M. , Yvenou E. , Simonato J.-P. , Carella A.
Published: July 2016

(BEDT-TTF)2I3nanoparticles of 2–6 nm have been isolated, and they exhibit a superconducting behaviour and encouraging thermoelectric properties.
Energy‐efficient cooperative two‐hop amplify‐and‐forward relay protocol in cognitive radio networks
Authors: Cai Caixia , Qiu Runhe
Published: July 2016

It has been shown that amplify‐and‐forward (AF) transmission is a viable transmission protocol for wireless networks incorporating distributed spatial diversity. However, a drawback of this relatively simple protocol is identified, the destination node is only to combine a part of the signal, while the other part of the signal has been regarded as interference for delay, leading to the lower utilisation of the resource inevitably, which manifests in the bigger noise, lower signal‐to‐noise ratio, and higher bit error rate. A revised AF relay protocol has been proposed for it could fully combine signal and eliminate delay at destination node through caching signal. A multi‐user single‐relay transmission model could demonstrate the superior performance of this protocol, which is in a hotspots region of a cognitive radio network. The closed‐form solution of the channel transmission rate is obtained with the form of matrix multiplication, and it can ensure that even if without any interference cancellation operation it still can improve the transmission rate. Analytical expression of downlink transmission energy efficiency (DLEE) has been derived. Numerical simulation results show that the transmission performances and DLEE have been improved by proposed protocol compared with the conventional AF relay protocol and direct transmission.
Impact analysis of the capacitive coupling sensor on bushing external insulation
Authors: Li Chengxiang , Xia Qi , Zhao Zhongyong , Yao Chenguo , Mi Yan , Zhao Xiaozhen , Wang Jian
Published: July 2016

Online impulse frequency response analysis (IFRA) method is proposed and developed as a new technique to detect the winding mechanical deformation of a running transformer. The preliminary application of IFRA has been realised by using the bushing capacitive coupling sensor (CCS). However, whether the installation of the sensor affects the normal operation of the transformer is still unknown. To study above problem, this study first establishes a simulation model for transformer bushing based on the finite‐element method and discusses the influence of sensor installation on the electric field distribution of capacitive bushing. The simulation proves that the installation of the CCS has minimal effect on the safe operation of the bushing. Second, the bushing withstand voltage tests are conducted in a lab, which proves that the installation of CCS meet the requirement for safe operation of capacitive bushing. Finally, the CCSs are installed on running power facilities, and the long and safe running experience indicates that the bushing and related facilities are unaffected by CCSs. The simulation analysis, withstand voltage test, and field application verify that the installation of CCS would not threaten the safe operation of high‐voltage bushing, laying the foundation for engineering application of IFRA.
Four Cases of Hemangiopericytoma and the Contribution of Radiotherapy in Their Management
Authors: Ilangovan Bhargavi , Sasikumar Neetu , Stumpf Janos , Devi Rathna , Venkatraman Murli , Kalyanaraman S. ,   Chendhilnathan
Published: July 2016

Hemangiopericytomas are tumors arising from the Zimmerman pericytes. They are characterized by their propensity to recur aggressively and metastasize. Surgery forms the primary treatment modality. Radiotherapy has been used in the postoperative setting and has proved to produce a significant progression-free survival in cases with residual disease. Radiotherapy has been applied even as a single modality treatment whenever surgery could not be performed. We are presenting four cases of meningeal hemangiopericytomas which have been treated with radiotherapy in combination with surgery. These cases show various scenarios in which Radiotherapy has been used in hemangiopericytoma: adjuvant setting, residual/recurrent setting, and in the palliative setting. As far as the technique is concerned, three-dimensional conformal radiotherapy, fractionated radiosurgery, and other forms of high-precision irradiation (intensity-modulated radiation therapy [IMRT]) were given.