Count Distribution for Generalized Weibull Duration with Applications

被引：5
|
作者：
Ong, S. H. [1 ]
Biswas, Atanu [2 ]
Peiris, S. [3 ]
Low, Y. C. [1 ]
机构：
[1] Univ Malaya, Inst Math Sci, Kuala Lumpur 50603, Malaysia
[2] Indian Stat Inst, Appl Stat Unit, Kolkata, India
[3] Univ Sydney, Sch Math & Stat, Sydney, NSW 2006, Australia
来源：
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | 2015年 / 44卷 / 19期
关键词：
Birth and renewal processes; Inter arrival times; Gamma distribution; Poisson distribution; Renewal function; Over and under dispersion; Laplace transform; Parameter estimation; Goodness-of-fit; Likelihood ratio test; RENEWAL FUNCTION; SERIES; MODELS;
D O I：
10.1080/03610926.2015.1062105
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
An extension of the Poisson distribution is derived by considering a stochastic point process where the duration has a generalized Weibull distribution. This distribution is able to represent under, equi and over dispersion, a useful feature in data analysis. The computation of the probabilities and renewal function (expected number of renewals) are examined. Parameter estimation by the method of maximum likelihood is considered with applications of the count distribution to real frequency count data exhibiting under and over dispersion. It is shown that the generalized Weibull count distribution fits much better than the Weibull and gamma duration models.
引用
收藏
页码：4203 / 4216
页数：14
相关论文
共 50 条
  • [1] A New Class of Generalized Modified Weibull Distribution with Applications
    Oluyede, Broderick O.
    Huang, Shujiao
    Yang, Tiantian
    AUSTRIAN JOURNAL OF STATISTICS, 2015, 44 (03) : 45 - 68
  • [2] Heterogeneous Weibull count distribution
    Karina, Tania M.
    Nurrohmah, Siti
    Fithriani, Ida
    INTERNATIONAL CONFERENCE ON MATHEMATICS: PURE, APPLIED AND COMPUTATION, 2019, 1218
  • [3] The generalized inverse Weibull distribution
    de Gusmao, Felipe R. S.
    Ortega, Edwin M. M.
    Cordeiro, Gauss M.
    STATISTICAL PAPERS, 2011, 52 (03) : 591 - 619
  • [4] Count Distribution for Mixture of Two Exponentials as Renewal Process Duration with Applications
    Low, Yeh Ching
    Ong, Seng Huat m
    INNOVATIONS THROUGH MATHEMATICAL AND STATISTICAL RESEARCH: PROCEEDINGS OF THE 2ND INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES AND STATISTICS (ICMSS2016), 2016, 1739
  • [5] On the Exponentiated Generalized Modified Weibull Distribution
    Aryal, Gokarna
    Elbatal, Ibrahim
    COMMUNICATIONS FOR STATISTICAL APPLICATIONS AND METHODS, 2015, 22 (04) : 333 - 348
  • [6] A GENERALIZATION OF WEIBULL DISTRIBUTION: THEORY AND APPLICATIONS
    Semary, Hatem E.
    Babu, M. Girish
    Elbatal, I.
    ADVANCES AND APPLICATIONS IN STATISTICS, 2022, 83 : 1 - 25
  • [7] STUDY OF A GENERALIZED WEIBULL DISTRIBUTION WITH OSCILLATORY FAILURE RATE
    Wang, Ronghua
    Gu, Beiqing
    Xu, Xiaoling
    Zhang, Shu-Yi
    JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2023, 13 (04): : 2326 - 2342
  • [8] The Weibull-Gamma Distribution: Properties and Applications
    Klakattawi, Hadeel S.
    ENTROPY, 2019, 21 (05)
  • [9] Weibull and Gamma Renewal Approximation Using Generalized Exponential Functions
    Jin, Tongdan
    Gonigunta, Lakshmana
    COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, 2009, 38 (01) : 154 - 171
  • [10] THE GAMMA-WEIBULL DISTRIBUTION
    Provost, Serge B.
    Saboor, Abdus
    Ahmad, Munir
    PAKISTAN JOURNAL OF STATISTICS, 2011, 27 (02): : 111 - 131
12345