New Log-Half-Cauchy distribution with Properties & Application to Lifetime Data
Journal Title: Journal of Advanced Research in Applied Mathematics and Statistics - Year 2018, Vol 3, Issue 3
Abstract
In this paper a new distribution based on Cauchy distribution called new log half-Cauchy distribution is proposed. This model is flexible enough to model different types of lifetime data having different forms of failure rate. The new distribution can accommodate both decreasing and increasing failure rates as its antecessors, as well as unimodal and bathtub shaped failure rates. Important mathematical properties including linear expansions for pdf and cdf of the log Half-Cauchy distribution are discussed. Furthermore some important statistical properties as mode, quantile function, skewness and kurtosis are studied. Rényi and q entropies of the new distribution are derived. The moments and incomplete moments of the new model are derived also the distributions of order statistics are discussed. The maximum likelihood estimation is used to evaluate the parameters involved. Simulation study has been conducted to study the accuracy and consistency of the MLE of the parameters. Finally, the usefulness of the new model for modeling reliability data is illustrated using a real data set to show the performance of the new distribution.
Authors and Affiliations
Saeed E. Hemeda
Keywords
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