Browsing by Author "Dey, S"

Now showing 1 - 4 of 4
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    Different Classical Methods of Estimation and Chi-squared Goodness-of- t Test for Unit Generalized Inverse Weibull Distribution
    (2021-07) khaoula, A; Dey, S; Kumar, D
    In this paper, we try to contribute to the distribution theory literature by incorporat ing a new bounded distribution, called the unit generalized inverse Weibull distribution (UGIWD) in the (0, 1) intervals by transformation method. The proposed distribution exhibits increasing and bathtub shaped hazard rate function. We derive some basic statis tical properties of the new distribution. Based on complete sample, the model parameters are obtained by the methods of maximum likelihood, least square, weighted least square, percentile, maximum product of spacing and Cramer-von-Mises and compared them using Monte Carlo simulation study. In addition, bootstrap condence intervals of the param eters of the model based on aforementioned methods of estimation are also obtained. We illustrate the performance of the proposed distribution by means of one real data set and the data set shows that the new distribution is more appropriate as compared to unit Birnbaum-Saunders, unit gamma, unit Weibull, Kumaraswamy and unit Burr III distri butions. Further, we construct chi-squared goodness-of- t tests for the UGIWD using right censored data based on Nikulin-Rao-Robson (NRR) statistic and its modi cation. The criterion test used is the modi ed chi-squared statistic Y 2, developed by Bagdon avicius and Nikulin (2011) for some parametric models when data are censored. The performances of the proposed test are shown by an intensive simulation study and an application to real data set
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    Inferences for generalized Topp-Leone distribution under dual generalized order statistics with applications to Engineering and COVID-19 data
    (2021) Kumar, D; Nassar, M; Dey, S
    This article accentuates the estimation of a two-parameter generalized Topp-Leone distribution using dual generalized order statistics (dgos). In the part of estimation, we obtain maximum likelihood (ML) estimates and approximate confidence intervals of the model parameters using dgos, in particular, based on order statistics and lower record values. The Bayes estimate is derived with respect to a squared error loss function using gamma priors. The highest posterior density credible interval is computed based on the MH algorithm. Furthermore, the explicit expressions for single and product moments of dgos from this distribution are also derived. Based on order statistics and lower records, a simulation study is carried out to check the efficiency of these estimators. Two real life data sets, one is for order statistics and another is for lower record values have been analyzed to demonstrate how the proposed methods may work in practice.
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    Power Modified Lindley Distribution: Properties, Classical and Bayesian Estimation and Regression Model with Applications
    (2023-07) Kumar, D; Dey, S; Kharazmi, O
    In this article, we explore a new probability density function, called the power modified Lindley distribution. Its main feature is to operate a simple trade-off among the general ized exponential, Weibull and gamma distributions, offering an alternative to these three well-established distributions. The proposed model turns out to be quite flexible: its probability density function can be right skewed and its associated hazard rate function may be increasing, decreasing, unimodal and constant. First the model parameters of the proposed distribution are obtained by the maximum likelihood method. Next, Bayes estimators of the unknown parameters are obtained under different loss functions. In addi tion, bootstrap confidence intervals are provided to compare with Bayes credible intervals. Besides, log power modified Lindley regression model for censored data is proposed. Two real data sets are analyzed to illustrate the flexibility and importance of the proposed model.
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    Statistical inference based on generalized Lindley record values
    (2019-10) Singh, S; Dey, S; Kumar, D
    This paper addresses the problems of frequentist and Bayesian estimation for the unknown parameters of generalized Lindley distribution based on lower record values. We first derive the exact explicit expressions for the single and product moments of lower record values, and then use these results to compute the means, variances and covariance between two lower record values. We next obtain the maximum likelihood estimators and associated asymptotic confidence intervals. Furthermore, we obtain Bayes estimators under the assumption of gamma priors on both the shape and the scale parameters of the generalized Lindley distribution, and associated the highest posterior density interval estimates. The Bayesian estimation is studied with respect to both symmetric (squared error) and asymmetric (linear-exponential (LINEX)) loss functions. Finally, we compute Bayesian predictive estimates and predictive interval estimates for the future record values. To illustrate the findings, one real data set is analyzed, and Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation and prediction.