توزيع جومبارتز– ميكهام المحول التكعيبي الخصائص والعزوم الخطية

Hamdan, Mohammed S (2020) توزيع جومبارتز– ميكهام المحول التكعيبي الخصائص والعزوم الخطية. Masters thesis, الجامعة الإسلامية – غزة شئون البحث العلمي والدراسات العليا -كلية العلوم دكتوراه العلوم الرياضية.

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Abstract

In this thesis, we introduce a new extension of the Gompertz-Makeham model which we will call "the cubic rank transmuted Gompertz-Makeham distribution." The proposed new model is an extended Gompertz-Makeham distribution generated by using a cubic rank transmutation map to add extra parameters to its distribution function. This new distribution is not found in any previous research papers. We will study its statisti- cal and mathematical properties, emphasizing its L-moments and probability weighted moments. Also, we have deduced relations between the L-moments of the cubic rank transmuted Gompertz-Makeham distribution with the probability weighted moments for Gompertz-Makeham distribution. Unusually, these relations have not been handled be- fore. Since who deal with L-moments deals with just computing. But, we have found relationships between them. Other properties that we have studied in this thesis include conventional moments, moment-generating function, order statistics, moments of order statistics, hazard rate function, quantile function, characteristic function, Shannon en- tropy, Renyi entropy, q-entropy, mean residual lifetime, maximum likelihood estimation of parameters. And through this, we have created many new relationships and theorems that have not been addressed by any of the authors before. Also, we use the methods of L-moments and maximum likelihood to estimate the parameters of CTGM distribution in samples generated from CTGM distribution. These methods of estimation of parameters are done using Mathematica packages. Finally, we use real data set to show that the cu- bic rank transmuted Gompertz-Makeham distribution is abetter �t than Kumaraswamy Pareto, Zografos-Balakrishnan log-logistic, Frechet and Gompertz-Makeham probability distributions.

Item Type: Thesis (Masters)
Subjects: Q Science > Q Science (General)
Depositing User: أ. دارين علي أحمد حمد
Date Deposited: 23 Nov 2020 11:20
Last Modified: 23 Nov 2020 11:20
URI: http://scholar.alaqsa.edu.ps/id/eprint/2612

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