Browsing by Author "Kumar, Devendra"

Now showing 1 - 11 of 11
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    Alpha logarithm transformed fréchetdistribution: Properties and estimation
    (Austrian Journal of Statistics, 2019) Dey, Sanku; Nassar, Mazen; Kumar, Devendra; Alaboud, Fahad
    In this paper, a new three-parameter distribution called the Alpha Logarithm Transformed Fr echet (ALTF) distribution is introduced which o ers a more exible distribution for modeling lifetime data. Various properties of the proposed distribu- tion, including explicit expressions for the quantiles, moments, incomplete moments, conditional moments, moment generating function R enyi and -entropies, stochastic ordering, stress-strength reliability and order statistics are derived. The new dis- tribution can have decreasing, reversed J-shaped and upside-down bathtub failure rate functions depending on its parameter values. The maximum likelihood method is used to estimate the distribution parameters. A simulation study is conducted to evaluate the performance of the maximum likelihood estimates. Finally, the pro- posed extended model is applied on real data sets and the results are given which illustrate the superior performance of the ALTF distribution compared to some other well-known distributions.
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    Inverse lindley power series distributions: anew compounding family and regressionmodel with censored data
    (Journal of Applied Statistics, 2022) Kumar, Devendra; Dey, Sanku; Shakhatren, Mohammed.k.
    This paper introduces a new class of distributions by compounding the inverse Lindley distribution and power series distributions which is called compound inverse Lindley power series (CILPS) distributions. An important feature of this distribution is that the lifetime of the component associated with a particular risk is not observable, rather only the minimum lifetime value among all risks is observable. Further, these distributions exhibit an unimodal failure rate. Various properties of the distribution are derived. Besides, two special models of the new family are investigated. The model parameters of the two sub-models of the new family are obtained by the methods of maximum likelihood, least square, weighted least square and maximum product of spacing and compared them using the Monte Carlo simulation study. Besides, the log compound inverse Lindley regression model for censored data is proposed. Three real data sets are analyzed to illustrate the flexibility and importance of the proposed models.
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    Modeling engineering data using extended power-Lindley distribution: Properties and estimation methods
    (Journal of King Saud University - Science, 2021) Al-Babtain, Abdulhakim A.; Kumar, Devendra; Gemeay, Ahmed M.; Dey, Sanku; Afify, Ahmed Z.
    In this paper, we introduce a new flexible distribution called the Weibull Marshall-Olkin power-Lindley (WMOPL) distribution to extend and increase the flexibility of the power-Lindley distribution to model engineering related data. The WMOPL has the ability to model lifetime data with decreasing, increasing, J-shaped, reversed-J shaped, unimodal, bathtub, and modified bathtub shaped hazard rates. Various properties of the WMOPL distribution are derived. Seven frequentist estimation methods are considered to estimate the WMOPL parameters. To evaluate the performance of the proposed methods and provide a guideline for engineers and practitioners to choose the best estimation method, a detailed simulation study is carried out. The performance of the estimators have been ranked based on partial and overall ranks. The performance and flexibility of the introduced distribution are studied using one real data set from the field of engineering. The data show that the WMOPL model performs better than some well-known extensions of the power-Lindley and Lindley distributions.
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    Moment Generating Functions of Complementary Exponential-Geometric Distribution Based on k-th Lower Record Values
    (Journal of Modern Applied Statistical Methods, 2018) Kumar, Devendra
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    Optimal test plan of Step-stress model of alpha power weibull lifetimes under progressively type-II censored samples
    (Symmetry, 2022) Alotaibi, Refah; Almetwally, Ehab M.; Kumar, Devendra; Rezk, Hoda
    In this study, the estimation of the unknown parameters of an alpha power Weibull (APW) distribution using the concept of an optimal strategy for the step-stress accelerated life testing (SSALT) is investigated from both classical and Bayesian viewpoints. We used progressive type-II censoring and accelerated life testing to reduce testing time and costs, and we used a cumulative exposure model to examine the impact of various stress levels. A log-linear relation between the scale parameter of the APW distribution and the stress model has been proposed. Maximum likelihood estimators for model parameters, as well as approximation and bootstrap confidence intervals (CIs), were calculated. Bayesian estimation of the parameter model was obtained under symmetric and asymmetric loss functions. An optimal test plan was created under typical operating conditions by minimizing the asymptotic variance (AV) of the percentile life. The simulation study is discussed to demonstrate the model’s optimality. In addition, real-world data are evaluated to demonstrate the model’s versatility.
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    Power Generalized Weibull Distribution with Applications in Engineering and Medicine
    (Journal of Statistical Theory and Applications, 2020) Kumar, Devendra
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    Relations for Moments of Generalized Order Statistics from Extended Exponential Distribution
    (AMERICAN JOURNAL OF MATHEMATICAL AND MANAGEMENT SCIENCES, 2017) Kumar, Devendra
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    Relations for moments of progressively type –II right censored order statistics from Erlang truncated exponential distribution.
    (American Journal of Mathematical and Management Sciences, 2017) Kumar, Devendra
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    Upper Record Values from Extended Exponential Distribution
    (Journal of Modern Applied Statistical Methods, 2018) Kumar, Devendra
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    The Weibull Marshall–Olkin Lindley distribution: properties and estimation
    (Journal of Taibah University for Science, 2020) Kumar, Devendra