Inference on Positive Exponential Family of Distributions (PEFD) through Transformation Method

Surinder  Kumar; Prem Lata  Gautam; Vaidehi  Singh

doi:10.13052/jrss0974-8024.13248

Surinder Kumar Department of Statistics, School for Physical and Decision Sciences, Babasaheb Bhimrao Ambedkar University, Lucknow-226025, India
Prem Lata Gautam Department of Statistics, School for Physical and Decision Sciences, Babasaheb Bhimrao Ambedkar University, Lucknow-226025, India
Vaidehi Singh Department of Statistics, School for Physical and Decision Sciences, Babasaheb Bhimrao Ambedkar University, Lucknow-226025, India

DOI: https://doi.org/10.13052/jrss0974-8024.13248

Keywords: Positive exponential family of distribution, uniformly minimum variance unbiased estimator, maximum likelihood estimator, confidence interval, probability of disaster, stress-strength reliability

Abstract

The estimation of R(t) and R = Pr(Y > X) for the Positive Exponential Family of Distribution
(PEFD) is considered. The UMVUE's, MLE's and Confidence Interval are derived.
These estimators are derived through the method of Transformation. The α = P(X > γ),
which is termed as probability of disaster is also derived when random stress X follows PEFD
and finite strength follows Power function distribution.

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Author Biographies

Surinder Kumar, Department of Statistics, School for Physical and Decision Sciences, Babasaheb Bhimrao Ambedkar University, Lucknow-226025, India

Surinder Kumar, Head, Department of Statistics, BBAU (A central University), Lucknow, India. He is having 26 years research experience in various research fields of Statistics such as Sequential Analysis, Reliability Theory, Business Statistics and Bayesian Inference. Prof. Kumar has published more than 60 research publications in various journals of national and international repute.

Prem Lata Gautam, Department of Statistics, School for Physical and Decision Sciences, Babasaheb Bhimrao Ambedkar University, Lucknow-226025, India

Prem Lata Gautam, Department of Statistics, BBAU (A Central University) Lucknow, India. She has research experiences of 6 years and has also published 6 research articles in various reputed journals in the field of Sequential analysis, Bayesian estimation and Reliability theory and wholesome knowledge of many softwares and language like R Software, Mathematica and Fortron.

Vaidehi Singh, Department of Statistics, School for Physical and Decision Sciences, Babasaheb Bhimrao Ambedkar University, Lucknow-226025, India

Vaidehi Singh, Department of Statistics, BBAU (A Central University), Lucknow, India. She has research experience of 6 years, her research areas are Sequential Analysis, Reliability Theory and Bayesian Inference. She has published more than 8 research articles in various National and International journals. She is working as an Assistant Professor in Lucknow and teaching the graduate and postgraduate students since last two and a half years.