A new class of power-Cauchy power series distribution for parallel systems: properties and inference with application to medical data: A new class of power-Cauchy power series distribution

Junaid Sarfraz; Shakeel Ahmed

doi:10.64497/jssci.233

Authors

Junaid Sarfraz Govt postgraduate college No 1 Abbottabad
Shakeel Ahmed Department of Statistics, Govt Postgraduate College No.1 Abbottabad

DOI:

https://doi.org/10.64497/jssci.233

Keywords:

power Cauchy, power series, compound distribution, maximum likelihood estimation, Bayesian estimation, geometric distribution, survival analysis

Abstract

In this paper, we propose a new three-parameter distribution with increasing, decreasing, unimodal, upside-down bathtub, and U-bathtub shaped failure rates. The resulting distribution is a compounding of the Power-Cauchy and Power Series called the Power-Cauchy Power Series (PCPS) distribution. We explored its several statistical properties. The efficiency of the maximum-likelihood estimators (MLEs) and Bayesian estimators (BEs) is examined by conducting a simulation study. Three sub-models in the new class of PCPS are provided. Finally, the usefulness of the model has been demonstrated by applying it to a real dataset.

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A new class of power-Cauchy power series distribution for parallel systems: properties and inference with application to medical data