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2016 - 201932020 - 20221
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Subject: Statistics × End date: 2022 × Type: Thesis × Thesis Type: M.Sc ×
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Now showing 1 - 4 of 4
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    ThesisItemOpen Access
    A study of weighted Lindley distribution: Bayesian approach
    (G. B. Pant University of Agriculture and Technology, Pantnagar, 2022-07) Fartyal, Sakshi; Vinod Kumar
    The present study proposes and investigates the distributional features of a new lifetime distribution known as the weighted Lindley distribution which has a single parameter θ. The Newton-Raphson method has been used to derive the maximum likelihood estimates of the parameter. The formulas for the moment generating function (mgf), cumulant generating function (cgf), characteristic function, moments, and several such features of the new weighted Lindley distribution have also been obtained. Tierney and Kadane approximation method has been used to derive Bayes estimators for its parameter (θ), reliability function R(t), and hazard rate function h(t) under three priors, uniform, exponential and gamma. The resulting findings have been demonstrated using various randomly produced data sets from the proposed model using simulation technique, with each sample replicated 10,000 times. The Bayes Risks have been estimated under Squared Error Loss Function (SELF). Two real life data sets have further been used to demonstrate its utility. It is finally concluded that gamma prior outperforms uniform prior and exponential prior for computing the Bayes estimates of the parameter θ, reliability function R(t) and hazard rate function h(t) of the proposed weighted Lindley distribution.
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    ThesisItemOpen Access
    Bayesian estimation in weighted x gamma distribution
    (G.B. Pant University of Agriculture and Technology, Pantnagar - 263145 (Uttarakhand), 2017-12) Agrawal, Priya; Vinod Kumar
    In the present study, a new lifetime distribution, named weighted xgamma distribution has been proposed and its distributional properties are investigated. The maximum likelihood estimates of the parameter θ have been obtained by means of Newton-Raphson method. The expressions for various distributional properties of weighted xgamma distribution including its moment generating function (mgf), cumulant generating function (cgf), characteristic function, moments etc. have been derived. The Bayes estimators of its parameter (θ), reliability function R(t) and hazard rate function h(t) are obtained using Tierney and Kadane method of approximation under two priors namely uniform and gamma. The results obtained have been illustrated by means of several randomly generated data sets from the proposed model, each sample replicated 10,000 times The Bayes Risks have been evaluated by using Squared Error Loss Function (SELF). A real life data set has also been used to establish its utility. It is concluded that gamma prior is superior to uniform prior for finding Bayes estimates of the parameter θ, reliability function R(t) and hazard rate function h(t) of the proposed weighted xgamma distribution.
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    ThesisItemOpen Access
    Analysis of weather parameters and climate change in districts of Uttarakhand
    (G.B. Pant University of Agriculture and Technology, Pantnagar - 263145 (Uttarakhand), 2017-06) Adhikari, Raksha; Ahmad, Haseen
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    ThesisItemOpen Access
    Bayes estimation in weibull distribution
    (G.B. Pant University of Agriculture and Technology, Pantnagar - 263145 (Uttarakhand), 2016-06) Joshi, Himanil; Vinod Kumar
    In the present study, Bayes estimators of the parameters α and β of 2-parameter Weibull distribution and its reliability function R(t) have been obtained using 2 priors by means of Tierney and Kadane method and the results obtained are illustrated by means of several random samples generated from the above said distribution through R software and two real data sets. It is revealed that when α is known, Bayes estimate (2.0074) of β is more precise for prior 2 compared to prior 1 at α=2.0, whereas Bayes estimate (0.5138) of R(t) is more precise for prior 2 compared to prior 1 at α=1.5 and initial time t=1.2. Further when β is known, Bayes estimates (1.5100) and (0.6446) of α and reliability function R(t=1.2) respectively are more precise for prior 2 compared to prior 1 at β=3.0. In case both parameters α and β are unknown, Bayes Risks of the estimates of α and R(t) under SELF are smaller for prior 2 compared to prior 1 for first three random samples generated from Weibull distribution with parameters (α=1.5, β=2.0); (α=1.5, β=3.0) and (α=2.0, β=2.5) respectively whereas Risk of the estimate of β is smaller for Prior 1 in case of these first three samples. Moreover, for the random sample generated from Weibull distribution with α=2.5, β=2.5, the risks of the estimates of β and R(t) are smaller for prior 1 compared to prior 2 and the risk of the estimate of α is smaller for prior 2 compared to prior 1. For two real data sets, prior 2 is superior to prior 1 for obtaining Bayes estimates (5.2788 and 4.8120) of α and Bayes estimates (191.6974 and 365.9996) of β which supports the conclusions drawn from the data generated through R software. Therefore, it is safer to use prior 2 compared to prior 1 for getting Bayes estimates of parameters α and β of 2 parameter Weibull distribution.