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The Complementary Exponentiated Lomax-Poisson Distribution with Applications to Bladder Cancer and Failure Data

Authors

  • Devendra Kumar Amity University Noida
  • Mazen Nassar Zagazig University
  • Ahmed Z. Afify Benha University
  • Sanku Dey St. Anthony’s College

Abstract

A new continuous four-parameter lifetime distribution is introduced by compounding the distribution of the maximum of a sequence of an independently identically exponentiated Lomax distributed random variables and zero truncated Poisson random variable, defined as the complementary exponentiated Lomax Poisson (CELP) distribution. The new distribution which exhibits decreasing and upside down bathtub shaped density while the distribution has the ability to model lifetime data with decreasing, increasing and upside-down bathtub shaped failure rates. The new distribution has a number of well-known lifetime special sub-models, such as Lomax-zero truncated Poisson distribution, exponentiated Pareto-zero truncated Poisson distribution and Pareto- zero truncated Poisson distribution. A comprehensive account of the mathematical and statistical properties of the new distribution is presented. The model parameters are obtained by the methods of maximum likelihood, least squares, weighted least squares, percentiles, maximum product of spacing and Cram\'er-von-Mises and compared them using Monte Carlo simulation study. We illustrate the performance of the proposed distribution by means of two real data sets and both the data sets show the new distribution is more appropriate as compared to the transmuted Lomax, beta exponentiated Lomax, McDonald Lomax, Kumaraswamy Lomax, Weibull Lomax, Burr X Lomax and Lomax distributions.

Author Biography

Devendra Kumar, Amity University Noida

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How to Cite

Kumar, D., Nassar, M., Z. Afify, A., & Dey, S. The Complementary Exponentiated Lomax-Poisson Distribution with Applications to Bladder Cancer and Failure Data. Austrian Journal of Statistics, 50(3), 77–105. Retrieved from https://ajs.or.at/index.php/ajs/article/view/1052