Browsing by Author "Vikas Kumar Sharma"

Now showing 1 - 20 of 34

A Bivariate Teissier Distribution: Properties, Bayes Estimation and Application
(Springer, 2024) Vikas Kumar Sharma; Sudhanshu Vikram Singh; Ashok Kumar Pathak
This article presents a bivariate extension of the Teissier distribution, whose univariate marginal distributions belong to the exponentiated Teissier family. Analytic expressions for the different statistical quantities such as conditional distribution, joint moments, and quantile function are explicitly derived. For the proposed distribution, the concepts of reliability and dependence measures are also explored in details. Both the maximum likelihood technique and the Bayesian approach are utilised in the process of parameter estimation for the proposed distribution with unknown parameters. Several numerical experiments are reported to study the performance of the classical and Bayes estimators for varying sample size. Finally, a bivariate data is fitted using the proposed distribution to show its applicability over the bivariate exponential, Rayleigh, and linear exponential distributions in real-life situations. © Indian Statistical Institute 2023.
A Family of Additive Teissier-Weibull Hazard Distributions for Modeling Bathtub-Shaped Failure Time Data
(World Scientific, 2023) Vikas Kumar Sharma; Sudhanshu Vikram Singh; Christophe Chesneau
The paper introduces a new failure time distribution called additive Teissier-Weibull distribution. Among its features, it is capable of modeling increasing and bathtub hazard rates. It is thus useful in modeling heterogeneous populations and can be viewed as the failure time model of the system having two modes of failures that follow the Teissier and Weibull distributions, respectively. Some of its important properties are obtained, such as quantiles, moments and shapes of the probability density and hazard functions. Four different methods of estimation such as the maximum likelihood, least squares, weighted least squares and maximum product spacing are proposed to estimate the unknown parameters. To compare the performance of the estimates, an extensive simulation study is carried out with varying sample sizes. Finally, failure times of primary reactor pumps and power generators are fitted and analyzed to show that the new additive hazard rate model may give a better fit than many other existing models. © 2023 World Scientific Publishing Company.
A new class of distributions as a finite functional mixture using functional weights
(Academia Brasileira de Ciencias, 2021) Dalal Lala Bouali; Christophe Chesneau; Vikas Kumar Sharma; Hassan S. Bakouch
In this paper, we introduce a new family of distributions whose probability density function is defined as a weighted sum of two probability density functions; one is defined as a warped version of the other. We focus our attention on a special case based on the exponential distribution with three parameters, a dilation transformation and a weight with polynomial decay, leading to a new life-time distribution. The explicit expressions of the moments generating function, moments and quantile function of the proposed distribution are provided. For estimating the parameters, the method of maximum likelihood estimation is used. Two applications with practical data sets are given. © 2021, Academia Brasileira de Ciencias. All rights reserved.
A New Class of Distributions for Modelling Continuous Positively Skewed Data Sets
(Thai Statistical Association, 2025) Nishant Kumar Srivastava; Sanjay Kumar Singh; Vikas Kumar Sharma; Umesh Singh
In this paper, we proposed a new class of distributions by introducing a new constant in the existing model. We discuss general properties of the family such as density function, quantile function and hazard rate function. We then discuss a member of the family considering the exponential distribution as baseline distribution. Various properties of the model such as quantile function, moments, moment generating function, order statistics, stress-strength parameter, and mean residual life function are discussed. We also discussed the mean, variance, skewness and kurtosis of the proposed model numerically. The expression for Rényi and Shannon entropies are also derived. The different methods of estimation such as maximum likelihood estimation, maximum product spacing and least squares estimates are used for the estimation of the unknown parameters of the proposed distribution.. The simulation study is performed to study the behaviour of the estimates based on their mean squared errors. Lastly, we apply our proposed model to two real data sets. © 2025, Thai Statistical Association. All rights reserved.
A new family of decreasing density and hazard quantile functions for modeling time-to-event data
(World Scientific, 2023) Komal Shekhawat; Vikas Kumar Sharma
In this paper, a convenient and parsimonious family of the quantile functions is proposed for modeling time-to-event data. Detailed mathematical arguments are presented for deriving the explicit expressions of the quantile density, quantile hazard and quantile mean remaining life functions. Their functional properties are also explored. Some important members of the family are provided. A special case, the so-called additive power logarithmic quantile family, is discussed with detailed properties, parameter estimation and application to time-to-event data. Measures of skewness and kurtosis for the proposed quantile function are derived. Important statistical measures useful for reliability analysis are also provided with their explicit expressions. Stochastic ordering, tail weight and order statistics are also discussed. L-moments are explicitly derived for the proposed quantile function. Estimation is approached using the likelihood function and percentiles. A real data set consists of times between occurrence of the coal-mining accidents is analyzed for illustration purposes. © World Scientific Publishing Company.
A new upside-down bathtub shaped hazard rate model for survival data analysis
(Elsevier Inc., 2014) Vikas Kumar Sharma; Sanjay Kumar Singh; Umesh Singh
In medical, engineering besides demography and other applied disciplines, it is pronounced in some applications that the hazard rate of the data initially increased to a pick in the beginning age, declined abruptly till it stabilized. In statistics literature, such hazard rate is known as the upside-down bathtub shaped hazard rate and propound in the various survival studies. In this paper, we proposed a transmuted inverse Rayleigh distribution, which possesses the upside-down bathtub shape for its hazard rate. The fundamental properties such as mean, variance, mean deviation, order statistics, Renyi entropy and stress-strength reliability of the proposed model are explored here. Further, three methods of estimation namely maximum likelihood, least squares and maximum product spacings methods are used for estimating the unknown parameters of the transmuted inverse Rayleigh distribution, and compared through the simulation study. Finally, the applicability of the proposed distribution is shown for a set of real data representing the times between failures of the secondary reactor pumps. © 2014 Elsevier Inc. All rights reserved.
Acute Febrile Illness in India: An Epidemiological Retrospective Study
(Bentham Science Publishers, 2025) Kaushalendra Kumar; Amit Kumar Tripathi; Vikas Kumar Sharma; Sunil Kumar Mishra; Ranjana Saksena Patnaik
Introduction: Acute febrile illness (AFI) is a frequent occurrence in India, often complicated by a multitude of pathogenic and etiological factors. In this context, it is important to analyze the biochemical, hematological, and epidemiological clinical parameters of AFI patients in the North Indian population. Methods: This study included 1,819 patients of various ages who presented with new-onset acute febrile illness (AFI) between 2017 and 2021. Among these patients, 211, with a median age of 40 years (ranging from 2 to 85 years), were selected for further analysis. At enrollment, clinical examination involved collecting respiratory tract specimens, blood, and urine samples for biochemical analysis, with subsequent data analysis conducted using statistical methods. Results and Discussion: The following biochemical parameters were analyzed: C-reactive protein (CRP), alkaline phosphatase (ALP), serum glutamate-pyruvate transaminase (SGPT), serum glutamic oxaloacetic transaminase (SGOT), gamma-glutamyl transpeptidase (GGT), and total protein serum. The hematological parameters included total leukocyte count (TLC), lymphocyte count, monocyte count, eosinophil count, red blood cell count (RBCs), packed cell volume (PCV), erythrocyte sedimentation rate (ESR), hematocrit value, mean corpuscular volume (MCV), and mean corpuscular hemoglobin (MCH). Additionally, clinical parameters such as phosphorus, urea, calcium, sodium, uric acid, bilirubin, and potassium were measured. Specific values observed were: SGPT (~113 IU/L in 2018), SGOT (~81 U/L in 2019), GGT (~148 g/L in 2018), and total protein serum (~7 g/L in 2020). The hematological parameters (TLC, lymphocyte, monocyte, RBCs, PCV, ESR, MCV, and MCH). The regression analysis was conducted to explore the temperature recorded at the time of admission, the duration of hospital stays, and biochemical as well as hematological variables of patients suffering from AFI. Karl-Pearson's correlation coefficient and variance inflation factor for each variable mentioned above. Conclusion: Biochemical and hematological parameters were analyzed over different years of intake in patients with Acute Febrile Illness (AFI). Further investigation is required to explore the mechanistic pathways of infection, and preventive measures will be implemented using natural products and other therapeutic interventions. Our data will offer the first systematic assessment of the etiological factors, along with regression analysis and the Karl-Pearson correlation coefficient for each variable in AFI patients. © 2025 Bentham Science Publishers.
An Extension of Exponentiated Gamma Distribution: A New Regression Model with Application
(Pleiades Publishing, 2022) Devendra Kumar; Vikas Kumar Sharma
Abstract: In this paper, we introduce a two parameter extension of exponentiated gamma distribution. We explicitly derive the closed form expressions of the moments, mode and quantiles of the proposed distribution. L-moments and coefficients of skewness and kurtosis are obtained using the quantile function. Other important properties including identifiability, entropy, stochastic orderings, stress-strength reliability and differential equations associated with the distribution are also discussed. We briefly describe different estimation procedures namely, the method of maximum likelihood estimation, moment estimation, maximum product of spacings estimation, ordinary and weighted least squares estimation, and Cramér–von-Mises estimation along with an extensive simulation study for comparing their performance. An application of modeling trees growth data is presented to show the adequacy of the proposed distribution over the distributions existing in the literature. A parametric regression model based on the proposed distribution is introduced and used to establish a regression model for the volume, diameter and height of the trees. © 2022, Pleiades Publishing, Ltd.
An Extension of J-Shaped Distribution with Application to Tissue Damage Proportions in Blood
(Springer, 2021) Komal Shekhawat; Vikas Kumar Sharma
In this paper, we introduce a two parameter extension of J-shaped distribution investigated by Topp and Leone (J. Am. Stat. Assoc. 50, 209–219, 1995) which is defined on the unit interval. We explicitly derive the closed-form expressions of the moments, mode and quantiles of the proposed distribution. L-moments and coefficients of skewness and kurtosis are obtained using the quantile function. Other important properties including identifiability, entropy, stochastic orderings, stress-strength reliability and differential equations associated with the distribution are also discussed. We construct maximum likelihood estimators to estimate the distribution parameters that are unknown for a given set of practical data. An extensive simulation study is carried out to study the behaviors of mean squared error, bias and absolute bias of the maximum likelihood estimators. An application of modeling tissue damage proportions in blood at various concentration levels of a drug is presented to show the adequacy of the proposed distribution over the unit range distributions existing in the literature. A parametric regression model based on the proposed distribution is introduced and the goodness-of-fit results are compared with that of Beta regression model. © 2020, Indian Statistical Institute.
Bayes estimation of defective proportion for single shot device testing data with information on masking and manufacturing defects
(SAGE Publications Ltd, 2024) Akanksha Kumari; Vikas Kumar Sharma
The present work addresses the problem of estimating the defective proportion of Single-Shot-Devices under the Bayesian paradigm while taking failure cause information into account. In addition, the maximum likelihood estimation is also presented. The logit transformation is suggested to use for defective proportion parameter for better stability of the numerical maximum likelihood estimate. The same transformation is used for the posterior distribution. Since the posterior distribution becomes complex, we propose the use of Metropolis-Hastings method to draw the posterior samples and present posterior sample based inferences. Bayes estimation under several symmetric and asymmetric loss functions is presented in this work. Predictive posterior density of future failures is also derived. The prior distributions of the model parameters are assumed to follow specific functional forms. A comprehensive simulation study is conducted to examine the performance of the estimates in relation to sample size and model parameters. Our study demonstrates that integrating combined information on masking and defective proportions is crucial for parameter estimation. To demonstrate the practical application of our proposed methodology, we apply it to skin cancer data using the linear failure rate model as survival distribution. © IMechE 2024.
Bayes estimation of defective proportion for single shot device testing data with information on masking and manufacturing defects
(SAGE Publications Ltd, 2025) Akanksha Kumari; Vikas Kumar Sharma
The present work addresses the problem of estimating the defective proportion of Single-Shot-Devices under the Bayesian paradigm while taking failure cause information into account. In addition, the maximum likelihood estimation is also presented. The logit transformation is suggested to use for defective proportion parameter for better stability of the numerical maximum likelihood estimate. The same transformation is used for the posterior distribution. Since the posterior distribution becomes complex, we propose the use of Metropolis-Hastings method to draw the posterior samples and present posterior sample based inferences. Bayes estimation under several symmetric and asymmetric loss functions is presented in this work. Predictive posterior density of future failures is also derived. The prior distributions of the model parameters are assumed to follow specific functional forms. A comprehensive simulation study is conducted to examine the performance of the estimates in relation to sample size and model parameters. Our study demonstrates that integrating combined information on masking and defective proportions is crucial for parameter estimation. To demonstrate the practical application of our proposed methodology, we apply it to skin cancer data using the linear failure rate model as survival distribution. © IMechE 2024
Bayesian analysis for Type-II hybrid censored sample from inverse Weibull distribution
(Springer, 2013) Sanjay Kumar Singh; Umesh Singh; Vikas Kumar Sharma
In this paper, we have discussed the Bayesian procedure for the estimation of the parameters of inverse Weibull distribution under Type-II hybrid censoring scheme. The highest posterior density credible intervals for the parameters have also been constructed. The performance of the Bayes estimators of the model parameters have been compared with maximum likelihood estimators through the Monte Carlo Markov chain techniques. Finally, two real data sets have been analysed for illustration purpose. © 2013 The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden.
Bayesian estimation and prediction for flexible Weibull model under type-II censoring scheme
(2013) Sanjay Kumar Singh; Umesh Singh; Vikas Kumar Sharma
We have developed the Bayesian estimation procedure for flexible Weibull distribution under Type-II censoring scheme assuming Jeffrey's scale invariant (noninformative) and Gamma (informative) priors for the model parameters. The interval estimation for the model parameters has been performed through normal approximation, bootstrap, and highest posterior density (HPD) procedures. Further, we have also derived the predictive posteriors and the corresponding predictive survival functions for the future observations based on Type-II censored data from the flexible Weibull distribution. Since the predictive posteriors are not in the closed form, we proposed to use the Monte Carlo Markov chain (MCMC) methods to approximate the posteriors of interest. The performance of the Bayes estimators has also been compared with the classical estimators of the model parameters through the Monte Carlo simulation study. A real data set representing the time between failures of secondary reactor pumps has been analysed for illustration purpose. © 2013 Sanjay Kumar Singh et al.
Bayesian estimation and prediction for the generalized Lindley distribution under asymmetric loss function
(Hacettepe University, 2014) Sanjay Kumar Singh; Umesh Singh; Vikas Kumar Sharma
The paper develops the Bayesian estimation procedure for the generalized Lindley distribution under squared error and general entropy loss functions in case of complete sample of observations. For obtaining the Bayes estimates, both non-informative and informative priors are used. Monte Carlo simulation is performed to compare the behaviour of the proposed estimators with the maximum likelihood estimators in terms of their estimated risks. Discussion is further extended to Bayesian prediction problem based on an informative sample where an attempt is made to derive the prediction intervals for future observations. Numerical illustrations are provided based on a real data example. © 2014, Hacettepe University. All rights reserved.
Bayesian estimation on interval censored Lindley distribution using Lindley’s approximation
(Springer, 2017) Vikas Kumar Sharma; Sanjay Kumar Singh; Umesh Singh; Khair Ul-Farhat
Interval censored data commonly arise in engineering and biomedical sciences. The present study deals with Bayesian estimation of interval censored lifetime data while it is assumed that lifetimes follow Lindley distribution. Assuming Jeffrey’s and gamma prior distributions, Bayes estimator of the Lindley parameter has been constructed under symmetric, squared error loss and asymmetric, general entropy loss functions. In addition, Bayes estimators for mean life, reliability and hazard rate have also been constructed. Since posterior distribution can not be reduced to any standard distribution, Lindley’s approximation technique has been utilized for Bayesian computations. The performances of the Bayes estimators has been compared with corresponding maximum likelihood estimators on the basis of simulated samples. Real data sets from engineering and biomedical fields have been analysed for illustration purposes. © 2016, The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden.
Bivariate extension of bathtub-shaped distribution
(Springer, 2022) Puneet Kumar Gupta; Pramendra Singh Pundir; Vikas Kumar Sharma; M. Mesfioui
Modeling of bathtub-shaped hazard rate function commonly arises in reliability and survival analyses. The present article introduces a bivariate extension of the Chen distribution that has bathtub-shaped hazard function. The proposed distribution has closed-form expressions for the joint survival function and conditional distributions. Several properties of the proposed distribution such as joint moments, marginals and conditional distributions are discussed. We obtain maximum likelihood estimators for estimating the unknown parameters using the expectation-maximization algorithm. At the end, application of the proposed distribution is illustrated by means of a real-life application. © 2022, The Author(s), under exclusive licence to Society for Reliability and Safety (SRESA).
Classical and Bayesian methods of estimation for power Lindley distribution with application to waiting time data
(Korean Statistical Society, 2017) Vikas Kumar Sharma; Sanjay Kumar Singh; Umesh Singh
The power Lindley distribution with some of its properties is considered in this article. Maximum likelihood, least squares, maximum product spacings, and Bayes estimators are proposed to estimate all the unknown parameters of the power Lindley distribution. Lindley's approximation and Markov chain Monte Carlo techniques are utilized for Bayesian calculations since posterior distribution cannot be reduced to standard distribution. The performances of the proposed estimators are compared based on simulated samples. The waiting times of research articles to be accepted in statistical journals are fitted to the power Lindley distribution with other competing distributions. Chi-square statistic, Kolmogorov-Smirnov statistic, Akaike information criterion and Bayesian information criterion are used to access goodness-of-fit. It was found that the power Lindley distribution gives a better fit for the data than other distributions. © 2017 The Korean Statistical Society, and Korean International Statistical Society.
Discussion comments on “Exponentiated Teissier distribution with increasing, decreasing and bathtub hazard functions”
(Taylor and Francis Ltd., 2024) Vikas Kumar Sharma; Sudhanshu V. Singh; Komal Shekhawat
In this note, we present some discussion comments on a note entitled ‘A note on the unimodality and log-concavity of the exponentiated Teissier distribution’ submitted in J. Appl. Stat. by some authors, about the paper by Sharma et al. (Exponentiated Teissier distribution with increasing, decreasing and bathtub hazard functions, J. Appl. Stat. 49 (2022), pp. 371–393). © 2023 Informa UK Limited, trading as Taylor & Francis Group.
Expected total test time and Bayesian estimation for generalized Lindley distribution under progressively Type-II censored sample where removals follow the Beta-binomial probability law
(2013) Sanjay Kumar Singh; Umesh Singh; Vikas Kumar Sharma
In this paper, we have proposed the progressive Type-II censoring scheme which allows the removals of the live units from a life-test with Beta-binomial probability law during the execution of the experiment. To stablish the theory, the generalized Lindley distribution is considered. For our proposed procedure, the behaviour of the expected total test time has been investigated through the numerical study. The classical as well as the Bayesian procedures for the estimation of the unknown model parameters have also been developed under this censoring scheme. Further, the discussion has been extended to the prediction of the future samples under Bayesian paradigm. Finally, a real data set has been analysed to illustrate the discussed methodology. © 2013 Elsevier Inc. All rights reserved.
Exponentiated Teissier distribution with increasing, decreasing and bathtub hazard functions
(Taylor and Francis Ltd., 2022) Vikas Kumar Sharma; Sudhanshu V. Singh; Komal Shekhawat
This article introduces a two-parameter exponentiated Teissier distribution. It is the main advantage of the distribution to have increasing, decreasing and bathtub shapes for its hazard rate function. The expressions of the ordinary moments, identifiability, quantiles, moments of order statistics, mean residual life function and entropy measure are derived. The skewness and kurtosis of the distribution are explored using the quantiles. In order to study two independent random variables, stress–strength reliability and stochastic orderings are discussed. Estimators based on likelihood, least squares, weighted least squares and product spacings are constructed for estimating the unknown parameters of the distribution. An algorithm is presented for random sample generation from the distribution. Simulation experiments are conducted to compare the performances of the considered estimators of the parameters and percentiles. Three sets of real data are fitted by using the proposed distribution over the competing distributions. © 2020 Informa UK Limited, trading as Taylor & Francis Group.