Browsing by Author "Harsh Tripathi"

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Generalized Inverse Xgamma Distribution: Properties, Estimation and Its Applications To Survival Data
(Thai Statistical Association, 2025) Harsh Tripathi; Abhimanyu Singh Yadav; Mahendra Saha; Sumit Kumar
This article introduces a new form of IXGD called the generalized inverse Xgamma distribution. The proposed model exhibits the pattern of an inverted bathtub type hazard rate and it belongs to the family of positively skewed models. The explicit expressions of some distributional properties, such as, moments, inverse moments, conditional moments, mean deviation, quantile function etc. are derived. To estimate the unknown model parameters as well as survival characteristics, viz., survival function and hazard rate function, we used different estimation procedures, namely, method of maximum likelihood estimation, ordinary and weighted least squares estimation, Cramer-von-Mises estimation and maximum product of spacings estimation. Also, the Bayesian estimation of the same is studied with respect to the squared error loss function. The asymptotic confidence intervals and the Bayes credible intervals of the parameters are computed. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation in terms of average mean squared errors for the point estimates, average widths and coverage probabilities for interval estimates. Finally, the potential and practical applicability of the proposed model is illustrated through two real life examples. © 2025, Thai Statistical Association. All rights reserved.
Reliability Test Plan Based on Logistic-Exponential Distribution and Its Application
(River Publishers, 2021) Abhimanyu Singh Yadav; Mahendra Saha; Shivanshi Shukla; Harsh Tripathi; Rajashree Dey
In this article, a reliability test plan is developed for Logistic-exponential distribution (LoED) under time truncated life test scheme. The distribution has been chosen because it can used to model lifetime of several reliability phenomenon and it performs better than many well known existing distributions. With the discussions of statistical properties of the aforesaid model, the reliability test plan has been established under the assumption of median quality characteristics when minimum confidence level P∗ is given. To quench the objective of the paper i.e; to serve as a guiding aid to the emerging practitioners, minimum sample sizes have been obtained by using binomial approximation and Poisson approximation for the proposed plan. Further, operating characteristic (OC) values for the various choices of quality level are placed. Also, minimum ratio of true median life to specified life has been presented for specified producer’s risk. Important findings of the proposed demonstrate the appropriateness of suggested reliability test plan is achieved using four real life situation. © 2021 River Publishers.
THE EXPONENTIATED XGAMMA DISTRIBUTION: A NEW MONOTONE FAILURE RATE MODEL AND ITS APPLICATIONS TO LIFETIME DATA
(University of Bologna, 2021) Abhimanyu Singh Yadav; Mahendra Saha; Harsh Tripathi; Sumit Kumar
In this article, the exponentiated version of xgamma distribution (XGD) has been introduced, named as exponentiated xgamma distribution (EXGD). The proposed model is positively skewed and possess some interesting shapes of hazard rate, i.e., increasing, decreasing and bathtub. Different distributional properties of proposed model, viz., moments, generating functions, mean deviation, quantile function, order statistics, reliability curves and indices etc. have been derived. The estimation of the parameters, survival function and hazard function of EXGD have been approached by different methods of estimation. A Simulation study is carried out to compare the performances of the different estimators obtained via different methods of estimation. Two real data sets have been analyzed to illustrate the applicability of the proposed model. © 2021 Statistica. All rights reserved.