Eulerian Binomial Type Revisited

This article presents the Poisson-Inverse Gamma regression model with varying dispersion for approximating heavy-tailed and overdispersed claim counts. Our main contribution is that we develop an Expectation-Maximization (EM) type algorithm for maximum likelihood (ML) estimation of the Poisson-Inverse Gamma regression model with varying dispersion. The empirical analysis examines a portfolio of motor insurance data in order to investigate the efficiency of the proposed algorithm. Finally, both the a priori and a posteriori, or Bonus-Malus, premium rates that are determined by the Poisson-Inverse Gamma model are compared to those that result from the classic Negative Binomial Type I and the Poisson-Inverse Gaussian distributions with regression structures for their mean and dispersion parameters.

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A linear algebra setting for the rota-mullin theory of polynomials of binomial type

Linear and Multilinear Algebra ◽

10.1080/03081087308817006 ◽

1973 ◽

Vol 1 (1) ◽

pp. 67-80 ◽

Cited By ~ 19

Author(s):

Jay P. Fillmore ◽

S.G. Williamson

Keyword(s):

Linear Algebra ◽

Binomial Type ◽

Polynomials Of Binomial Type

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Sequences of Symmetric Functions of Binomial Type

Studies in Applied Mathematics ◽

10.1002/sapm19908311 ◽

1990 ◽

Vol 83 (1) ◽

pp. 1-30 ◽

Cited By ~ 6

Author(s):

Daniel E. loeb

Keyword(s):

Symmetric Functions ◽

Binomial Type

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Polynomials of binomial type and Lucas’ Theorem

Proceedings of the American Mathematical Society ◽

10.1090/proc/12849 ◽

2015 ◽

Vol 144 (5) ◽

pp. 1897-1904 ◽

Cited By ~ 1

Author(s):

David Goss

Keyword(s):

Binomial Type ◽

Polynomials Of Binomial Type

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Test Environment-Dependent Discrete Binomial-Type Software Reliability Models

International Journal of Reliability Quality and Safety Engineering ◽

10.1142/s0218539317500036 ◽

2017 ◽

Vol 24 (01) ◽

pp. 1750003 ◽

Cited By ~ 1

Author(s):

Shinji Inoue ◽

Shigeru Yamada

Keyword(s):

Software Reliability ◽

Information Criterion ◽

Test Environment ◽

Environment Factors ◽

Reliability Models ◽

Testing Phase ◽

Modeling Approach ◽

Software Reliability Models ◽

Binomial Type ◽

Mean Square Errors

We have no doubt that the software reliability growth process in the testing phase depends on the test environment factors, such as the attained testing coverage, the number of test-runs and the debugging skills, which affect the software failure occurrence or fault detection phenomenon in the testing phase. In this paper, we propose software reliability models that consider the effects of the testing environment factors. Our models are developed by a program size-dependent discrete binomial-type software reliability modeling approach. This modeling approach is also consistent with software reliability data collection and enables us to consider the effect of the program size. Finally, we compare the accuracy of our models in terms of mean square errors (MSE) and Akaike’s information criterion (AIC) with the existing corresponding model by using actual data.

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Joint distributions of successes, failures and patterns in enumeration problems

Advances in Applied Probability ◽

10.1239/aap/1013540248 ◽

2000 ◽

Vol 32 (3) ◽

pp. 866-884 ◽

Cited By ~ 21

Author(s):

S Chadjiconstantinidis ◽

D. L. Antzoulakos ◽

M. V. Koutras

Keyword(s):

Joint Distribution ◽

Joint Probability ◽

Fixed Number ◽

Composite Pattern ◽

Joint Distributions ◽

Special Cases ◽

Enumeration Problems ◽

Binomial Type ◽

Probability Mass ◽

Mass Functions

Let ε be a (single or composite) pattern defined over a sequence of Bernoulli trials. This article presents a unified approach for the study of the joint distribution of the number Sn of successes (and Fn of failures) and the number Xn of occurrences of ε in a fixed number of trials as well as the joint distribution of the waiting time Tr till the rth occurrence of the pattern and the number STr of successes (and FTr of failures) observed at that time. General formulae are developed for the joint probability mass functions and generating functions of (Xn,Sn), (Tr,STr) (and (Xn,Sn,Fn),(Tr,STr,FTr)) when Xn belongs to the family of Markov chain imbeddable variables of binomial type. Specializing to certain success runs, scans and pattern problems several well-known results are delivered as special cases of the general theory along with some new results that have not appeared in the statistical literature before.

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