Browsing by Author "Umesh Singh"

Now showing 1 - 20 of 75

A comparative study of traditional and kullback-leibler divergence of survival functions estimators for the parameter of lindley distribution
(Austrian Statistical Society, 2019) Sultan Parveen; Sanjay Kumar Singh; Umesh Singh; Dinesh Kumar
A new point estimation method based on Kullback-Leibler divergence of survival functions (KLS), measuring the distance between an empirical and prescribed survival functions, has been used to estimate the parameter of Lindley distribution. The simulation studies have been carried out to compare the performance of the proposed estimator with the corresponding Least square (LS), Maximum likelihood (ML) and Maximum product spacing (MPS) methods of estimation. © 2019, Austrian Statistical Society. All rights reserved.
A new asymmetric loss function for estimation of any parameter
(DAV College, 2020) Dinesh Kumar; Pawan Kumar; Pradip Kumar; Umesh Singh; Prashant Kumar Chaurasia
A new asymmetric loss function which is suitable for estimation of location as well as scale and other parameters has been introduced. To check the superiority of the proposed loss function over some existing and exploited loss functions such as squared error loss function (SELF), general entropy loss function (GELF), LINEX loss function and Logarithmic-SELF (LSELF), we have calculated the Bayes estimators of the parameterθ of exponential distribution under SELF, GELF, LINEX loss function, Logarithmic- SELF (LSELF) and the proposed exponential squared error loss function (ESELF) for complete sample from the exponential distribution. A data set has been considered to show its application to the real problems. The simulation study is carried out to compare the performance of Bayes estimators in terms of their posterior risks. © 2020 DAV College. 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 distribution with monotone and non-monotone shaped failure rate
(ISOSS Publications, 2020) Sandeep K. Maurya; Sanjay K. Singh; Umesh Singh
In the present paper, we propose to use a transformation to get a new class of distribution by using some baseline distribution. We have considered Lindley distribution as baseline model which is a popular model used in the field of reliability and engineering. The proposed model includes various shapes like increasing, decreasing and bathtub failure rates. We have studied its statistical properties along with the maximum likelihood estimation procedure for the estimation of parameters of the proposed model. Lastly, three real data sets are used to compare the suitability of the proposed model over seven other existing models. © 2020, ISOSS Publications. All rights reserved.
A new lifetime distribution: Some of its statistical properties and application
(Natural Sciences Publishing, 2018) Dinesh Kumar; Umesh Singh; Sanjay Kumar Singh; Prashant Kumar Chaurasia
In the present paper, a new lifetime distribution has been introduced by the use of Minimum Guarantee transformation as suggested by Kumar et al. (2017). For the purpose, Lindley distribution is considered as a baseline distribution. Some of the statistical properties of this distribution has been studied and classical estimators like maximum likelihood estimator (MLE), least square estimator (LSE) and maximum product of spacing estimator (MPSE) has been obtained and their performance is carried out through simulation study. Further, a real data has been taken to show its application in the real scenario. ©2018 NSP Natural Sciences Publishing Cor.
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.
Admissibility of a test procedure based on preliminary test of significance for life data
(1989) S.K. Singh; S.K. Upadhyay; Umesh Singh
Necessary and sufficient condition for admissibility of a test procedure based on preliminary test of significance for life data has been obtained. © 1989.
Analysis and prediction of COVID-19 spreading through Bayesian modelling with a case study of Uttar Pradesh, India
(Springer, 2022) Deepmala; Nishant Kumar Srivastava; Sanjay Kumar Singh; Umesh Singh
Predicting the dynamics of COVID-19 cases is imperative to enhance the health care system’s capacity, monitor the effects of policy interventions, and control the transmission. With this view, this paper examines the transmission process of the COVID-19 employing three types of confirmed, deceased, and recovered cases in Uttar Pradesh, India. We demonstrated an approach that has the power to sufficiently predict the number of confirmed, deceased, and recovered cases of COVID-19 in the near future, given the past occurrences. We used the logistic and Gompertz non-linear regression model under the Bayesian setup. In this regard, we built the prior distribution of the model using information obtained from some other states of India, which have already reached the advanced stage of COVID-19. This analysis did not consider any changes in government control measures. © 2022, The Author(s), under exclusive licence to Operational Research Society of India.
Assessing the effect of E-Bayesian inference for Poisson inverse exponential distribution parameters under different loss functions and its application
(Taylor and Francis Ltd., 2022) Anurag Pathak; Manoj Kumar; Sanjay Kumar Singh; Umesh Singh
This paper present E-Bayesian and Bayesian estimators of parameters of Poisson inverse exponential distribution (PIED) under Squared error loss function (SELF), General entropy loss function (GELF) and Linear Exponential loss function (LINEX) for progressive type-II censored data with binomial removals (PT-II CBRs). The E-Bayesian and corresponding Bayesian estimators are compared in terms of their risks based on simulated samples from PIED. The proposed methodology is applied to survival time of multiple myeloma patients data. © 2020 Taylor & Francis Group, LLC.
Bayes Estimator of Generalized-Exponential parameters under Linex loss function using Lindley's approximation
(Ubiquity Press Ltd, 2008) Rahul Singh; Sanjay Kumar Singh; Umesh Singh; Gyan Prakash Singh
In this paper, we have obtained the Bayes Estimator of Generalized- Exponential scale and shape parameter using Lindley 's approximation (L-approximation) under asymmetric loss functions. The proposed estimators have been compared with the corresponding MLE for their risks based on simulated samples from the Generalized-Exponential distribution.
Bayes estimator of inverse Gaussian parameters under general entropy loss function using lindley's approximation
(2008) P.K. Singh; S.K. Singh; Umesh Singh
In this article, we obtained Bayes estimators of parameters of Inverse Gaussian distributions under asymmetric loss function using Lindley's Approximation (L-Approximation). The proposed estimators have been compared with the corresponding estimators obtained under symmetric loss function and MLE for their risks. This comparison is illustrated using Monte-Carlo study of 2,000 simulated sample from the Inverse Gaussian distribution.
Bayes estimators for two parameter exponential distribution
(1995) Rajesh Singh; S.K. Upadhyay; Umesh Singh
The present paper gives the Bayes estimators of the parameters for two parameter exponential distribution using independent priors. The risks of the proposed estimators under quadratic loss have been compared with those of the estimators based on conjugate prior, It has been concluded that unless there is a strong reason to believe the dependent structure in priors, independent priors may be used. © 1995, Taylor & Francis Group, LLC. All rights reserved.
Bayes estimators of exponential parameters from a censored sample using a guessed estimate
(Ubiquity Press Ltd, 2008) G.P. Singh; S.K. Singh; Umesh Singh; S.K. Upadhyay
This paper provides the Bayes estimators of the failure rate and reliability function for a one-parameter, exponential distribution by utilizing a point guess estimate of the parameter. For deriving the Bayes estimators, the prior distributions are chosen such that they are centered at the known prior values of parameters. The validity of proposed estimators is examined with respect to their maximum likelihood estimators (MLE) and Thompson's Shrinkage estimator on the basis of Monte Carlo simulations of 1000 samples.
Bayes estimators of exponential parameters utilizing a guessed guarantee with specified confidence
(1994) Umesh Singh; S.K. Upadhyay; Rajesh Singh
This paper proposes a procedure to modify the conjugate prior for the parameters of an exponential distribution in the light of an available guessed guarantee μ0 with specified confidence c (0
Bayes estimators of the reliability function and parameter of inverted exponential distribution using informative and non-informative priors
(2013) Sanjay Kumar Singh; Umesh Singh; Dinesh Kumar
In this paper, we propose Bayes estimators of the parameter and reliability function of inverted exponential distribution under the general entropy loss function for complete, type I and type II censored samples. The proposed estimators have been compared with the corresponding maximum-likelihood estimators for their simulated risks (average loss over sample space). © 2013 2013 Taylor & Francis.
Bayes interval for the Weibull parameters utilizing guessed estimates
(1993) S.K. Singh; Umesh Singh; S.K. Upadhyay
In this paper an attempt is made to provide a method of obtaining the HPD-intervals for the scale and shape parameters of the Weibull distribution, when a prior distribution of the parameter places a weight (1 - b) on the guess value of the parameter and distributes the rest probability mass b according to some specified distribution. The equal tail credible intervals have been obtained and it is proposed that these limits be used as initial points for obtaining the HPD-intervals. © 1993.
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 for inverse weibull distribution under progressive type-II censored data with beta-binomial removals
(Austrian Statistical Society, 2018) Pradeep K. Vishwakarma; Arun Kaushik; Aakriti Pandey; Umesh Singh; Sanjay K. Singh
This paper deals with the estimation procedure for inverse Weibull distribution under progressive type-II censored samples when removals follow Beta-binomial probability law. To estimate the unknown parameters, the maximum likelihood and Bayes estimators are obtained under progressive censoring scheme mentioned above. Bayes estimates are obtained using Markov chain Monte Carlo (MCMC) technique considering square error loss function and compared with the corresponding MLE’s. Further, the expected total time on test is obtained under considered censoring scheme. Finally, a real data set has been analysed to check the validity of the study. © 2018, Austrian Statistical Society. All rights reserved.