Ann. Data. Sci. https://doi.org/10.1007/s40745-018-0165-0 The Hyperbolic Sine Rayleigh Distribution with Application to Bladder Cancer Susceptibility Zubair Ahmad Received: 19 March 2018 / Revised: 29 April 2018 / Accepted: 18 May 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract In this paper, a new extension of the Rayleigh distribution called the Hyper- bolic Sine-Rayleigh distribution is introduced and studied. The proposed model is very ﬂexible and is capable of modeling with increasing and unimodal hazard rates. A com- prehensive treatment of its mathematical properties including explicit expressions for the moments, quantiles, moment generating function, Entropy and order statistics are provided. Maximum likelihood estimates of the model parameters are obtained. Fur- thermore, a simulation study is conducted to access the behavior of the maximum likelihood estimators. Finally, the superiority of the subject model is illustrated empir- ically over the other distributions by analyzing a real-life application. Keywords Hyperbolic sine function · Rayleigh distribution · Entropy · Moments · Order statistics · Maximum likelihood estimates 1 Introduction In fact, statistical distributions are very convenient and useful in predicting real-world phenomena. Therefore, in the last couple of decades or so, an extensive research works have done in the literature on
Annals of Data Science – Springer Journals
Published: May 28, 2018
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