Statistical Inference for the Unit Gompertz Power Series Distribution Using Ranked Set Sampling with Applications

Abstract

We present the unit Gompertz-power series distribution class, which is formedby combining unit Gompertz and power series distributions. This new class of distributionsincludes some special cases, such as the unit Gompertz binomial, the unit Gompertz Poisson, the unit Gompertz geometric, and the unit Gompertz logarithmic distributions. Thenew class’s mathematical properties, such as quantiles, moments, generating function, orderstatistics, and Renyi entropy are investigated. The unit Gompertz-power series distribution’ssub-models are thoroughly examined. The maximum likelihood and Bayesian methodologiesare 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 highlightthe 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.