Devendra Kumar

• Ph.D.
• Professor (Associate) at University of Delhi

In this paper, we consider the problem of estimating the unknown parameters of a generalized half-normal (GHN) distribution when lifetime data are observed from accelerated life test (ALT) experiments in the presence of hybrid censoring. To relate the lifetime of products under different stress levels, we make use of a cumulative exposure model (CE...

Inverse Weibull, lognormal, and inverse Gaussian are some commonly used statistical distributions for modeling positively skewed failure lifetime data. These distributions share some interesting properties among themselves like they all have uni‐modal hazard rates. In this paper, we address the problem of discriminating among these statistical dist...

Accelerated life test experiments aim to generate lifetime data in a short time for the further statistical analysis, and are very useful when the units under experiment are highly reliable. Statistical analysis for lifetime data observed from accelerating life testing in presence of some censoring becomes a challenging task. In this paper, we cons...

Order statistic plays an important role in statistical theoretical and practical problems. In this paper, we derive algebraic expressions for both single and product moments of order statistics from generalized Topp-Leone (GTL) distribution. These expressions will be useful for computational purposes. Further, based on order statistics, we have obt...

The log-normal and the log-logistic distributions are two of the most commonly used distributions for studying positively skewed lifetime data. Both the distributions share number of interesting properties, and for a certain range of parameters their cumulative and hazard functions can also be similar in nature. However, selecting a more appropriat...

This article aims to describe some statistical properties of the power generalized Weibull distribution along with some parametric estimation methods. An extensive simulation study is carried out to assess the effectiveness of the estimation of model parameters using numerous well known classical methods of estimation. Next, the Bayes estimators of...

In this paper, the estimation of the unknown parameters of inverted modified Lindley distribution using the concept of dual generalized order statistics (dgos) is investigated from both classical and Bayesian viewpoints. Based on this considered distribution, first, the maximum likelihood estimator (MLE) and approximate confidence interval of the m...

Accelerated life testing has been used frequently in several fields as it provides an economical way for obtaining failure time data rapidly or in a shorter time as compared to normal operating conditions. The lifetime data of a product at a constant stress level are assumed to have an exponentiated power Lindley distribution, and the model's shape...

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...

The modified power function distribution is an important distribution for analyzing the lifetime data, which is quite flexible and can be used effectively in modeling survival data. It can have increasing, decreasing, upside-down bathtub and bathtub shaped failure rate. In this paper, we derive the exact explicit expressions for the single and doub...

Based on record values and inter-record times, this paper develops inference procedures for the estimation of the parameters of generalized inverted exponential distribution (GIED). First, based on inverse and random sampling schemes, we derive the maximum likelihood estimators (MLEs) and associated asymptotic confidence intervals of the unknown pa...

We propose a new bounded distribution called the Marshall-Olkin reduced Kies distribution, which is a competitive model to the generalized beta, Kumaraswamy and beta distributions. It is able to model both negative and positive skewed data. Eight classical estimation methods are used to estimate its parameters. A simulation study is conducted to co...

The power generalized Weibull distribution has been proposed recently by [24] as an alternative to the gamma, Weibull and the exponentiated Weibull distributions. The power generalized Weibull family is suitable for modeling data that indicate nonmonotone hazard rates and can be used in survival analysis and reliability studies. Usefulness and flex...

In this paper, we propose inference procedures for the estimation of parameters by using order statistics. First, we derive some new expressions for single and product moments of the order statistics from the extended power Lindley distribution. We then use these moments to obtain the best linear unbiased estimates (BLUEs) of the location and scale...

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 generalized exponential, Weibull and gamma distributions, offering an alternative to these three well-established distributions. The proposed model turns out to be quite flexible...

Exponentiated Kumaraswamy-Power function (EKPF) distribution has been proposed recently by Bursa and Ozel (2017) as a quite flexible in terms of probability density and hazard rate functions than power function distribution. In this paper, we obtain the explicit expressions for the single, double (product), triple and quadruple moments and moment g...

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,...

In manufacturing industries and several other fields, accelerated life testing is used widely to obtain sufficient failure time data of test units quickly as compared to normal use conditions. It is assumed that the lifetime of a product at constant stress level follows generalized inverse Lindley distribution. It is a common observation that while...

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 onl...

In health related studies, we sometimes come across left-skewed heavy-tailed survival data and vary often the probability distributions proposed in the literature to fit the model of such survival data is not adequate. In this article, we explore a new probability density function with bounded domain. The new distribution arises from the Lomax dist...

Based on progressive Type-II censored samples, we first derive the recurrence relations for the single and product moments of progressively Type-II censored order statistics from two parameter Rayleigh distribution. These recurrence relations enable us to compute the mean and variances of all progressively Type-II censored order statistics for all...

A new continuous four-parameter lifetime distribution is introduced by compounding the distribution of the maximum of a sequence of an independently identically exponentiated Lomax distributed random variables and zero truncated Pois-son random variable, defined as the complementary exponentiated Lomax Poisson (CELP) distribution. The new distribut...

The uniqueness of this study comes from the fact that we provide explicit expressions.

A comprehensive review of transmuted distributions is provided. Nearly thirty such distributions are reviewed. Real data applications are provided comparing the reviewed distributions to other classes of distributions. This review could serve as an important reference and encourage developments of further transmuted distributions that could model c...

To study the heterogeneous nature of lifetimes of certain mechanical or engineering processes , a mixture model of some suitable lifetime distributions may be more appropriate and appealing as compared to simple models. This paper considers mixture of Topp-Leone distributions under classical and Bayesian perspective based on complete sample. The ne...

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 value...

Mazucheli et al. (2019) introduced a new transformed model called the unit-Gompertz (UG) distribution which exhibits right-skewed (uni-modal) and reversed-J shaped density and its hazard rate function can be increasing and increasing-decreasing-increasing. They worked on the estimation of the model parameters based on complete data sets. In this pa...

In this paper, we try to contribute to the distribution theory literature by incorporating 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 statisti...

In this paper, we try to contribute to the distribution theory literature by incorporating 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 statisti...

In this paper, a new probability density function with bounded domain is presented. The new distribution arises from the Lindley distribution proposed in 1958. It presents the advantage of not including any special function in its formulation. The new transformed model, called the reflected-shifted-truncated Lindley distribution can be used to mode...

In this paper, we obtained several recurrence relations for the single and product moments under progressively Type-II right censored order statistics and then use these results to compute the means and variances of two parameter reduced Kies distribution. Besides, these moments are then utilized to derived best linear unbiased estimators of the sc...

In this paper a new probability density function with bounded domain is presented. The new distribution arises from the Lindley distribution proposed by Lindley (1958). It presents the advantage of not including any special function in its formulation. The new transformed model, called the reflected-shifted-truncated Lindley distribution can be use...

In this paper, we try to supplement the distribution theory literature by incorporating a new bounded distribution, called the bounded weighted exponential (BWE) distribution in the (0, 1) intervals by transformation method. The proposed distribution exhibits decreasing and left-skewed unimodal density while the hazard rate can have increasing and...

Exponentiated power Lindley distribution is proposed as a generalization of some widely well-known distributions such as Lindley, power Lindley and generalized Lindley distributions. In this paper, the exact explicit expressions for moments of order statistics from the exponentiated power Lindley distribution are derived. By using these relations,...

In this paper, we first derive the exact explicit expressions for the single and product moments of order statistics from the type-II exponentiated log-logistic distribution, and then use these results to compute the means, variances, skewness and kurtosis of rth order statistics. Besides, best linear unbiased estimators (BLUEs) for the location an...

Based on progressively Type-II right censored order statistics, we establish several recurrence relations for the single and product moments from the generalized Pareto distribution due to Pikands (1975). Further, recursive computational algorithm is provided which enable us to compute all the means, variances and covariances for all sample sizes n...

This paper proposes a new flexible four-parameter model called Marshall-Olkin power generalized Weibull (MOPGW) distribution which provides symmetrical, reversed-J shaped, left-skewed and right-skewed densities, and bathtub, unimodal, increasing, constant, decreasing, J shaped, and reversed-J shaped hazard rates. Some of the MOPGW structural proper...

This article addresses the problem of deriving the explicit expressions for single and product moments of order statistics, generalized order statistics and dual generalized order statistics from the generalized Lindley distribution. The means and variances of order statistics, lower record values and progressively type-II censored order statistics...

In this article, we provide a comprehensive account of the mathematical properties of the weighted inverted Weibull distribution. Furthermore, we compare different methods of estimation of the unknown parameters of a three-parameter Weighted Inverted Weibull distribution (WIWD) from the frequentist points of view. These methods include the maximum...

We introduce a new lifetime distribution, called the alpha-power transformed extended exponential distribution which generalizes the extended exponential distribution proposed by Nadarajah and Haghighi (Statistics 45:543–558, 2011) to provide greater flexibility in modeling data from a practical point of view. The new model includes the exponential...

We obtain some properties of the Weibull Marshall-Olkin Lindley distribution. Its hazard rate function can be increasing, decreasing, bathtub-shaped, decreasing-increasing-decreasing and unimodal. We compare the performance of some methods to estimate its model parameters by means of extensive simulations. The potentiality of the new distribution t...

We introduce a new lifetime distribution, called the Alpha-Power Transformed extended exponential distribution which generalizes the extended exponential distribution proposed by Nadarajah and Haghighi (2011) to provide greater flexibility in modeling data from a practical point of view. The new model includes the exponential; extended exponential,...

The Lindley distribution has been generalized by many authors in recent years. A new two-parameter distribution with decreasing failure rate is introduced, called Alpha Power Transformed Lindley (�PTL) distribution that provides better fits than the Lindley distribution and some of its known generalizations. The new model includes the Lindley distr...

The generalized Lindley distribution is an important distribution for analyzing the stress–strength reliability models and lifetime data, which is quite flexible and can be used effectively in modeling survival data. It can have increasing, decreasing, upside-down bathtub and bathtub shaped failure rate. In this paper, we derive the exact explicit...

In this paper, exponentiated exponential-geometric distribution is considered. Some new explicit expressions for single and product moment of generalized order statistics based on a random sample drawn from the considered distribution are derived. The results for order statistics and upper records as special cases are obtained. Some new explicit ex...

We introduce a new lifetime distribution, called the Alpha-Power Transformed Lomax (APTL) Distribution which generalizes the Lomax distribution to provide better fits than the Lomax distribution and some of its known generalizations. Various properties of the proposed distribution, including explicit expressions for the quantiles, mode, moments, co...

Exponentiated Kumaraswamy-Power function (EKPF) distribution has been proposed recently by Bursa and Ozel (2017) as a quite flexible in terms of probability density and hazard rate functions than power function distribution. In this paper, we obtain the explicit expressions for the single, double (product), triple and quadruple moments and moment g...

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 betw...

In this article, we provide a comprehensive account of the mathematical properties of the weighted inverted Weibull distribution. Furthermore, we compare different methods of estimation of the unknown parameters of a three-parameter Weighted Inverted Weibull distribution (WIWD) from the frequentist points of view. These methods are, maximum likelih...

We introduce a new lifetime distribution namely, transmuted extended exponential distribution which generalizes the extended exponential distribution proposed by Nadarajah and Haghighi (Statistics 45:543–558, 2011) with an additional parameter using the quadratic rank transmutation map which was studied by Shaw and Buckley (The alchemy of probabili...

In this paper, exact expressions and some recurrence relations satisfied by marginal and joint moment generating function of lower generalized order statistics from generalized exponential distribution are derived. Further, the results are deduced for order statistics and lower record values. In the last section, a characterization Theorem based on...

In this paper, we have considered the generalized Pareto distribution. Various structural properties of the distribution are derived including (quantile function, explicit expressions for moments, mean deviation, Bonferroni and Lorenz curves and Renyi entropy). We have provided simple explicit expressions and recurrence relations for single and pro...

The extended exponential distribution has been proposed recently by Nadarajah and Haghighi (2011) as an alternative to the gamma, Weibull and the exponentiated exponential distributions. For this distribution, some recurrence relations are established for the single and product moments of upper record values. We also derive recurrence relations for...

We introduce the Marshal-Olkin alpha power family of distributions to extend the alpha power transformed exponential distribution defined by Mahdavi and Kundu (2017) and several other distributions. The new family is analytically tractable and it can be used quite effectively for data analysis. Some structural properties of the proposed family are...

Power Lindley distribution has been proposed recently by Ghitany et al. (Comput Stat Data Anal 64:20–33, 2013) as a simple and useful reliability model for analysing lifetime data. This model provides more flexibility than the Lindley distribution in terms of the shape of the density and hazard rate functions as well as its skewness and kurtosis. F...

In this paper a new probability density function with bounded domain is presented. This distri- bution arises from the Marshall-Olkin extended exponential distribution proposed by Marshall and Olkin (1997). It depends on two parameters and can be considered as an alternative to the classical beta and Kumaraswamy distributions. It presents the advan...

In this paper we introduce a new method for generating distributions which we refer to as logarithm transformed (LT) method. Some statistical properties of the LT method are established. Based on the LT method we introduce a new generalization of the Lomax distribution that provides better fits than the Lomax distribution and some of its known gene...

Based on progressive type-II censored samples, we first derive the recurrence relations for the single and product moments and then use these results to compute the means and variances of reduced Kies distribution (RKD), a new distribution, recently introduced by Kumar and Dharmaja (2013). Next, we obtain the maximum likelihood estimators of the un...

The Weibull distribution has been generalized by many authors in recent years. Here, we introduce a new generalization of the Weibull distribution, called Alpha logarithmic trans- formed Weibull distribution that provides better fits than some of its known generalizations. The proposed distribution contains Weibull, exponential, logarithmic transfo...

In this paper we, considered a Dagum distribution which is proposed by Dagum (1977) as income distribution. Some new simple explicit expressions and recurrence relations satisfied by the quotient moments of dual generalized order statistics based on a random sample drown from the considered distribution are derived. Further, applications of these r...

The complementary exponential-geometric (CEG) distribution is a useful model for analyzing lifetime data. For this distribution, some recurrence relations satisfied by marginal and joint moment generating functions of k-th lower record values were established. They enable the computation of the means, variances, and covariances of k-th lower record...

The power Lomax distribution due to Rady et al. (2016) is an alternative to and provides better �ts for bladder cancer data (see Lee and Wang (2003)) than the Lomax, exponential Lomax, Weibull Lomax, extended Poisson Lomax and beta Lomax distributions. Exact explicit expressions as well as recurrence relations for the single and double (product) mo...

The power generalized Weibull distribution due to Bagdonovacius and Nikulin (2002) is an alternative, and always provides better �ts than the exponentiated Weibull family for modeling lifetime data. In this paper, we consider the generalized order statistics (GOS) from this distribution. We obtain exact explicit expressions as well as recurrence re...

RNA-Seq has gained immense popularity and emerged as a potential high-throughput platform for identification of differentially expressed (DE) genes. In order to estimate the nature of differential genes, it is important to find statistical distributional property of the data. In the present study we propose a new hybrid model (NBPFCROS) based on pa...

The Lindley distribution has been generalized by many authors in recent years. A new two-parameter distribution is introduced, called Alpha Power Transformed Lindley (αP T L) distribution that provides better fit than the Lindley distribution and some of the well known distributions. The new model includes the Lindley distribution as a special case...

The inverse Lindley distribution has been generalized by many authors in recent years. Here, we introduce a new generalization called alpha power transformed inverse Lindley (APTIL) distribution that provides better fits than the inverse Lindley distribution and some of its known generalizations. The new model includes the inverse Lindley distribut...

This article addresses the various properties and different methods of estimation of the unknown parameters of Gompertz distribution. Although, our main focus is on estimation from both frequentist and Bayesian point of view, yet, various mathematical and statistical properties of the Gompertz distribution (such as quantiles, moments, moment genera...

In this paper, a new three-parameter distribution called the Alpha Logarithm Transformed Fr�echet (ALTF) distribution is introduced which offers a more exible distribution for modeling lifetime data. Various properties of the proposed distribution, including explicit expressions for the quantiles, moments, incomplete moments, conditional moments, m...

Based on progressively Type-II right censored order statistics values, we first derive the exact explicit expressions as well as recurrence relations for the single and product moments and then use these results to compute the means and variances of the extended exponential (EE) distribution due to Nadarajah and Haghighi (2011). These relations gen...

In this paper, we establish some new recurrence relations for the single and product moments of progressively Type-II right censored order statistics from the Erlangtruncated exponential distribution. These relations generalize those established by Aggarwala and Balakrishnan (1996) for standard exponential distribution. These recurrence relations e...

This article addresses various properties and estimation methods for the Exponentiated Chen Distribution. Although, our main focus is on estimation from frequentist point of view, yet, some statistical and reliability characteristics for the model are derived. We briefly describe different estimation procedures namely, the method of maximum likelih...

In this paper, a new three-parameter distribution, called α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} logarithmic transformed generalized e...

We introduce for the first time a new lifetime distribution namely, transmuted exponentiated Pareto (TEP) distribution which generalizes the exponentiated Pareto distribution proposed by Gupta et al. (1998) with an additional parameter using the quadratic rank transmutation map which was studied by Shaw and Buckley (2009) to provide greater flexibi...

The extended exponential distribution due to Nadarajah and Haghighi (2011) is an alternative and always provides better fits than the gamma, Weibull and the generalized exponential distributions whenever the data contains zero values. In this paper, we consider the generalized order statistics (GOS) from this distribution. We obtain exact explicit...

In this paper, exact expressions and some recurrence relations satisfied by marginal and joint moment generating function of lower generalized order statistics from generalized exponential distribution are derived. Further, the results are deduced for order statistics and lower record values. In the last section, a characterization Theorem based on...

In this paper, we considered the type I generalized half logistic distribution and derived some explicit expressions and recurrence relations for the marginal and joint moment generating function of generalized order statistics from the type I generalized half logistic distribution. The results for order statistics and record values are deduced fro...

In this paper, we have established several explicit expressions and recurrence relations for single and product moments of -th lower record values from exponentiated Burr XII distribution. Two characterizing results of exponentiated Burr XII distribution has been obtained by using the recurrence relation for single moments and conditional expectati...

In this paper, we have considered the exponentiated Pareto type I distribution. Various structural properties of the exponentiated Pareto type I distribution (such as quantile func- tion, moments, incomplete moments, conditional moments, mean deviation about mean and median, stochastic ordering, Bonferroni and Lorenz curves, Renyi entropy and order...

This article addresses the various mathematical and statistical properties of the Burr type XII distribution (such as quantiles, moments, moment generating function, hazard rate, conditional moments, mean residual lifetime, mean past lifetime, mean deviation about mean and median, stochasic ordering, stress-strength parameter, various entropies, Bo...

In this article, we establish recurrence relations for the single and product moments of order statistics from the power generalized Weibull (PGW) distribution due to Bagdonova ˜cius and Nikulin (2002). These recurrence relations enable computation of the means, variances and covariances of all order statistics for all sample sizes in a simple and...

This article addresses the problem of frequentist estimation of the parameters of the Kumaraswamy-Burr III distribution using upper record values. The explicit expressions and recurrence relations satisfied by the single and product moments of kth upper record values from Kumaraswamy-Burr III distribution are also derived. The corresponding results...

The dual generalized order statistics is a unified model which contains the well known decreasingly ordered random variables like order statistics and lower record values. With this definition we give simple expressions for single and product moments of dual generalized order statistics from Dagum distribution. The results for order statistics and...

In this paper, a new three-parameter distribution, called alpha logarithmic transformed Generalized Exponential Distribution (ALTGE) is proposed. The distribution has simple closed forms pdf and cdf. Various properties of the proposed distribution, including explicit expressions for the moments, quantiles, moment generating function, mean deviation...

The Singh–Maddala distribution is very flexible and most widely used for modeling the income, wage, expenditure and wealth distribution of the country. Several mathematical and statistical properties of this distribution (such as quantiles, moments, moment generating function, hazard rate, mean residual lifetime, mean deviation about mean and media...

In this paper, a new distribution, called �􀀀power transformed Generalized Exponential Dis- tribution (Alpha-PTGE) is proposed. The distribution has simple closed forms pdf and cdf. Several properties of the Alpha-PTGE distribution are studied including unimodality, moments, conditional moments, stochastic ordering and Shannon entropy. The distribut...

Based on lower record values, we first derive the exact explicit expressions as well as recur- rence relations for the single and product moments of record values and then use these results to compute the means, variances and coefficient of skewness and kurtosis of exponentiated moment exponential distribution (EMED), a new extension of moment expo...

The complementary exponential-geometric distribution is a useful model for analyzing lifetime data. For this distribution, we established some recurrence relations satisfied by marginal and joint moment generating functions of kth lower record values. These recurrence relations enable the computation of the means, variances and covariances of kth l...

In this article, we generalize the gamma mixed Rayleigh distribution using the quadratic rank transmutation map studied by Shaw et al. (2009) to develop a transmuted gamma mixed Rayleigh (TGMR) distribution. We provide a comprehensive description of the mathematical and statistical properties of the subject distribution. We briefly describe differ...

The extended exponential distribution due to Nadarajah and Haghighi (2011 S. Nadarajah and F. Haghighi, An extension of the exponential distribution. Statistics, 45 (2011), 543–558.) is an alternative to and always provides better fits than the gamma, Weibull and the exponentiated exponential distributions whenever the data contains zero values. We...

In this paper, we obtain recurrence relations for single and product moments of generalized order statistics based on random samples drawn from generalized Pareto distribution. Further, we deduce moments of order statistics and records values. Characterization of this distribution has also been considered using the conditional moments of the genera...