Binomial type distributions and multinomial distributions

Author(s):  
Robert A. Rigby ◽  
Mikis D. Stasinopoulos ◽  
Gillian Z. Heller ◽  
Fernanda De Bastiani
Keyword(s):  
1976 ◽  
Vol 31 (4) ◽  
pp. 618-633 ◽  
Author(s):  
Jay R. Goldman ◽  
J. T. Joichi ◽  
David L. Reiner ◽  
Dennis E. White
Keyword(s):  

Risks ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 97
Author(s):  
George Tzougas

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.


Author(s):  
Shinji Inoue ◽  
Shigeru Yamada

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.


1981 ◽  
Vol 64 (1) ◽  
pp. 89-93 ◽  
Author(s):  
David L. Reiner
Keyword(s):  

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