The Beta Modified Exponential Power Series Distribution: Properties and Applications
We propose a novel parametric distribution, termed the Beta Modified Exponential Power Series (BMEPS) distribution, capable of modeling increasing, decreasing, bathtub-shaped, and unimodal failure rates. Constructed from addressing a latent complementary risk problem, this distribution arises from a combination of the Beta Modified Exponential (BME) and power series distributions. Within this new distribution, several important distributions discussed in the literature, such as the Beta Modified Exponential Poisson (BMEP), Beta Modified Exponential Geometric (BMEG), and Beta Modified Exponential Logarithmic (BMEL) distributions, exist as special submodels. This work provides a comprehensive mathematical treatment of the new distribution, offering closed-form expressions for its density, cumulative distribution, survival function, failure rate function, the r-th raw moment, and moments of order statistics. Furthermore, we delve into maximum likelihood estimation and present formulas for the elements comprising the Fisher information matrix. Finally, to showcase the flexibility and potential applicability of the new distribution, we apply it to a real dataset.
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A COMPARATIVE STUDY ON THE RELATIONSHIP BETWEEN STATISTICS AND DATA SCIENCE
Amirhossein Ghatari *, Elham Tabrizi, Ehsan Bahrami Samani
Towards Mathematical Sciences, -
A Note on the Identifiability of General Bayesian Gaussian Models
Amirhossein Ghatari*, Ashkan Shabbak, Elham Tabrizi
Journal of Statistical Research of Iran, Summer and Autumn 2019