共查询到20条相似文献,搜索用时 12 毫秒
1.
F. De Vylder 《Insurance: Mathematics and Economics》1985,4(3):163-172
Let X be a random vector with distribution depending on a parameter treated as a random variable ?. The usual linear regression assumption is that E(X|?) can be displayed in the form yβ(?) where y is a fixed design matrix and β(?) an unknown vector. In the present paper we assume that E(X|?) is a rather arbitrary function ?(β(?)) of the unknown vector β(?) and we derive credibility approximations for β(?). 相似文献
2.
F. De Vylder 《Insurance: Mathematics and Economics》1982,1(1):35-40
We develop a stochastic multiplicative model for the forecasting of IBNR claims. The factor depending on the accident year is credibility adjusted.The title of this note also suits for the papers by Straub (1971) and Kramreiter and Straub (1973). We made stronger assumptions simplifying drastically the numerical calculations and the parameter estimation problem.As showed in the numerical illustrations, the developed method is also applicable in case of scarce irregular data. 相似文献
3.
A survey of credibility theory 总被引:26,自引:0,他引:26
Baoding Liu 《Fuzzy Optimization and Decision Making》2006,5(4):387-408
This paper provides a survey of credibility theory that is a new branch of mathematics for studying the behavior of fuzzy
phenomena. Some basic concepts and fundamental theorems are introduced, including credibility measure, fuzzy variable, membership
function, credibility distribution, expected value, variance, critical value, entropy, distance, credibility subadditivity
theorem, credibility extension theorem, credibility semicontinuity law, product credibility theorem, and credibility inversion
theorem. Recent developments and applications of credibility theory are summarized. A new idea on chance space and hybrid
variable is also documented. 相似文献
4.
P. G. Moschopoulos 《Annals of the Institute of Statistical Mathematics》1985,37(1):541-544
Summary The distribution of the sum ofn independent gamma variates with different parameters is expressed as a single gamma-series whose coefficients are computed
by simple recursive relations. 相似文献
5.
Maolin Pan 《Insurance: Mathematics and Economics》2008,42(1):119-126
In this paper, we investigate the problems of convergence of experience-based ratemakings regarding the Esscher principle. In addition to the Bayes and the classical credibility premiums, we suggest a new credibility formula for the Esscher premium. Then we show the convergence of the Bayes and the newly defined credibility premiums towards the individual premium and point out that the classical credibility premium does not generally converge to the individual premium by presenting a sufficient and necessary condition under which the classical credibility Esscher premium converges to the individual premium. A simulation study is carried out to illustrate the theoretical conclusions. 相似文献
6.
In this article, we derive the distribution of partially exchangeable binary random variables, generalizing the distribution of exchangeable binary random variables and hence the binomial distribution. The distribution can be viewed as a mixture of Markov chains. We introduce rectangular complete monotonicity and show that partial exchangebility can be characterized by rectangular complete monotonicity. The distribution aided with rectangular complete monotonicity can be used to analyze serially correlated data common in many areas of science. 相似文献
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Demetrios L. Antzoulakos Andreas N. Philippou 《Annals of the Institute of Statistical Mathematics》1996,48(3):551-561
The probability distribution functions (pdf's) of the sooner and later waiting time random variables (rv's) for the succession quota problem (k successes and r failures) are derived presently in the case of a binary sequence of order k. The probability generating functions (pgf's) of the above rv's are then obtained directly from their pdf's. In the case of independent Bernoulli trials, expressions for the pdf's in terms of binomial coefficients are also established. 相似文献
9.
Víctor Pérez-Abreu 《Periodica Mathematica Hungarica》2006,52(1):47-65
Summary The Gaussian unitary ensemble is a random matrix model (RMM) for the Wigner law. While random matrices in this model are infinitely
divisible, the Wigner law is infinitely divisible not in the classical but in the free sense. We prove that any variance mixture
of Gaussian distributions -- whether infinitely divisible or not in the classical sense -- admits a RMM of non Gaussian infinitely
divisible random matrices. More generally, it is shown that any mixture of the Wigner law admits a RMM. A key role is played
by the fact that the Gaussian distribution is the mixture of Wigner law with the <InlineEquation ID=IE"1"><EquationSource
Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>2$-gamma
distribution. 相似文献
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Recently (see De Vylder & Goovaerts (1984), this issue) so called credibility matrices have been introduced and studied in the framework of general properties of matrices, such as non-negativity, total positivity etc. In the present note we characterize a class of credibility matrices generated by the normed sequence of functions (pl, pl,…, pn) on K = [0, b] where , i=0, …, n, θ ? K, and where ?, g, h are nonnegative (eventually depending on n, n may be finite or infinite). For simplicity we suppose h to be monotonic and continuous. 相似文献
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15.
As in earlier works, we consider {0,1}n as a sample space with a probability measure on it, thus making pseudo-Boolean functions into random variables. Under the assumption that the coordinate random variables are independent, we show it is very easy to give an orthonormal basis for the space of pseudo-Boolean random variables of degree at most k. We use this orthonormal basis to find the transform of a given pseudo-Boolean random variable and to answer various least squares minimization questions. 相似文献
16.
Dr. P. J. Holewijn 《Probability Theory and Related Fields》1969,14(2):89-92
Summary This paper deals with the almost sure uniform distribution (modulo 1) of sequences of random variables. In the case where the law of the increments X
n+h
–X
n
of the sequence X
0, X
1, does not depend on n, sufficient conditions are given to assure the uniform distribution (modulo 1) with probability one. As an illustrative example the partial sums of a sequence of independent, identically distributed variables is considered. 相似文献
17.
S. V. Astashkin 《Mathematical Notes》2010,87(1-2):15-22
We prove a rather general comparison principle for the distribution functions of random variables. As a consequence, we obtain a criterion for the equivalence in distribution in the vector sense of an arbitrary sequence of random variables to the Rademacher system; we study the applications of this principle to special cases. 相似文献
18.
John Panaretos 《Annals of the Institute of Statistical Mathematics》1981,33(1):191-198
Summary LetX, Y be two discrete random variables with finite support andX≧Y. Suppose that the conditional distribution ofY givenX can be factorized in a certain way. This paper provides a method of deriving the unique form of the marginal distribution
ofX (and hence the joint distribution of (X, Y)) when partial independence only is assumed forY andX−Y. 相似文献
19.
L. B. Klebanov 《Journal of Mathematical Sciences》1990,52(2):2903-2905
It is shown that, under sufficiently general conditions, from the mean values of the minima of a random number of independent, identically distributed random variables, the distribution of the latter can be restored.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 166, pp. 60–62, 1988. 相似文献
20.
Some fundamental properties of the empirical distribution functions are derived in the case of mixing random variables. These properties are then utilized to study asymptotic normality and strong laws of large numbers for functions of order statistics. 相似文献