Statistical Inference for the Unit Gompertz Power Series Distribution Using Ranked Set Sampling with Applications | ||
| Assiut University Journal of Multidisciplinary Scientific Research | ||
| Volume 53, Issue 1, January 2024, Pages 154-189 PDF (1.2 M) | ||
| Document Type: Novel Research Articles | ||
| DOI: 10.21608/aunj.2023.246431.1068 | ||
| Authors | ||
| Manal Yousef* 1; Amal Hassan2; Ehab Almetwally3 | ||
| 1New Valley university | ||
| 2Faculty of Graduate Studies for Statistical Research, Cairo University, Giza | ||
| 3Faculty of Business Administration, Delta University for Science and Technology, Gamasa | ||
| Abstract | ||
| We present the unit Gompertz-power series distribution class, which is formed by combining unit Gompertz and power series distributions. This new class of distributions includes some special cases, such as the unit Gompertz binomial, the unit Gompertz Poisson, the unit Gompertz geometric, and the unit Gompertz logarithmic distributions. The new class’s mathematical properties, such as quantiles, moments, generating function, order statistics, and Renyi entropy are investigated. The unit Gompertz-power series distribution’s sub-models are thoroughly examined. The maximum likelihood and Bayesian methodologies are used to estimate the model parameters for the complete sample and ranked set sampling. The Bayesian estimation approach under the squared error and linear exponential loss functions is examined. Finally, we demonstrate applications of two real data sets to highlight the adaptability and potential of the one sub-model in the new class of distributions. Keywords: Unit Gompertz distribution; ranked set sampling; order statistics; linex loss function; Metropolis-Hastings; power series distribution. | ||
| Keywords | ||
| Keywords: Unit Gompertz distribution; ranked set sampling; order statistics; Metropolis-Hastings; power series distribution | ||
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