Statistical inference based on generalized Lindley record values
Journal of Applied Statistics, Oct 30, 2019
This paper addresses the problems of frequentist and Bayesian estimation for the unknown paramete... more 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.
Bayesian Estimation of Erlang Distribution Under Different Prior Distributions
This paper addresses the problem of Bayesian estimation of the parameters of Erlang distribution ... more This paper addresses the problem of Bayesian estimation of the parameters of Erlang distribution under squared error loss function by assuming different independent informative priors as well as joint priors for both shape and scale parameters. The motivation is to explore the most appropriate prior for Erlang distribution among different priors. A comparison of the Bayes estimates and their risks for different choices of the values of the hyperparameters is also presented. Finally, we illustrate the results using a simulation study as well as by doing real data analysis.
Mazucheli et al. introduced a new transformed model referred as the unit-Weibull (UW) distributio... more Mazucheli et al. introduced a new transformed model referred as the unit-Weibull (UW) distribution with uni-and anti-unimodal, decreasing and increasing shaped density along with bathtub shaped, constant and non-decreasing hazard rates. Here we consider inference upon stress and strength reliability using different statistical procedures. Under the framework that stress-strength components follow UW distributions with a known shape, we first estimate multicomponent system reliability by using four different frequentist methods. Besides, asymptotic confidence intervals (CIs) and two bootstrap CIs are obtained. Inference results for the reliability are further derived from Bayesian context when shape parameter is known or unknown. Unbiased estimation has also been considered when common shape is known. Numerical comparisons are presented using Monte Carlo simulations and in consequence, an illustrative discussion is provided. Two numerical examples are also presented in support of this study. Significant conclusion: We have investigated inference upon a stress-strength parameter for UW distribution. The four frequentist methods of estimation along with Bayesian procedures have been used to estimate the system reliability with common parameter being known or unknown.
Journal of Statistical Computation and Simulation, 2019
In this article, we propose eight different methods of estimation to estimate the unknown paramet... more In this article, we propose eight different methods of estimation to estimate the unknown parameters and the PCI Spmk for the log-logistic distribution from the frequentist point of view. Next, we consider three bootstrap confidence intervals namely, standard bootstrap, percentile bootstrap and student's t bootstrap for obtaining confidence intervals of the PCI Spmk using the aforementioned methods of estimation. Monte Carlo simulations are performed to compare the performances of coverage probabilities, average widths and relative coverage of the bootstrap confidence intervals using the proposed methods of estimation for both small and moderate samples. Besides, we have incorporated tolerance cost function in the index Spmk to develop a new cost effective PCI Spmkc. Additionally, the performances of the estimators have been compared in terms of their mean squared error using simulated samples. Finally, two real data sets are analyzed for illustrative purposes.
Communications in Statistics - Simulation and Computation, 2018
The process capability index, C pk , is a useful tool for assessing the capability of a manufactu... more The process capability index, C pk , is a useful tool for assessing the capability of a manufacturing process. There exist three well-known confidence intervals for the process capability index. These intervals are based on the standard bootstrap, the percentile bootstrap and the bias-corrected percentile bootstrap, respectively. We propose three variants of these bootstrap confidence intervals where each of the three intervals are modified in a particular way. Extensive Monte Carlo simulations are carried out and the results indicate that the three proposed bootstrap methods are generally preferred over the corresponding original schemes.
Journal of Computational and Applied Mathematics, 2018
In this paper, we introduce the Marshal-Olkin alpha power family of distributions to extend the a... more In this paper, we introduce the Marshal-Olkin alpha power family of distributions to extend the alpha power transform class defined by and several other distributions. The new family is analytically tractable and it can be used quite effectively for real data analysis. Some of its structural properties are established. Members of the new family can have symmetrical, right-skewed and reversed-J shaped densities, and increasing, decreasing, upside-down bathtub and reversed-J shaped hazard rates. The model parameters are obtained by the method of maximum likelihood estimation. We illustrate the performance of the proposed new family of distributions by means of three real data sets and the data sets show the new family of distributions is more appropriate as compared to the Marshall-Olkin generalized Lindley, Marshall-Olkin generalized exponential, Marshall-Olkin logistic exponential, Marshall-Olkin exponential, exponentiated exponential, transmuted generalized exponential, alpha power exponential and exponential distributions.
Journal of Scientific Research of the Banaras Hindu University, 2022
introduced logisticexponential (LE) distribution which has varied applications in lifetime modell... more introduced logisticexponential (LE) distribution which has varied applications in lifetime modellings. In this article, we consider parametric bootstrap control charts (BCCs) for detecting a shift in the percentile of LE distribution in a process monitoring situation. Four parametric BCCs based on maximum likelihood method, method of least squares, method of Cramèr-von-Mises and method of maximum product of spacings are used for monitoring percentiles of LE distribution. We perform simulations to see the performances of the proposed four BCCs with respect to average run length. Finally, one data set is analyzed to illustrate our results.
The power Lomax distribution due to is an alternative to and provides better fits for bladder can... more The power Lomax distribution due to is an alternative to and provides better fits for bladder cancer data (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) moments have been derived from the power Lomax distribution. These recurrence relations enable computation of the mean, variance, skewness and kurtosis of all order statistics for all sample sizes in a simple and efficient manner. By using these relation, the mean, variance, skewness and kurtosis of order statistics for sample sizes up to 5 for various values of shape and scale parameters are tabulated. Finally, remission times (in months) of bladder cancer patients have been analyzed to show how the proposed relations work in practice
In this article, we use multilevel multinomial logistic regression model to identify the risk fac... more In this article, we use multilevel multinomial logistic regression model to identify the risk factors of anemia in children of northeastern States of India. The data consisted of 10,136 children of age group 6-59 months. We considered the level of anemia as the outcome variable with four ordinal categories (severe, moderate, mild, and non-anemic) based on hemoglobin concentration in blood as per WHO guidelines. A two-level random intercept model was considered with state of residence as the level-2 variable. The intra-class correlation (ICC) between states is 0.0577 indicating approximately 6% of the total variation in the response variable accounted for by the state of residence. Several multilevel models have been compared, and a final model was decided based on deviance test. We observed that predicted probability of being at or below severely anemic level to be 0.1247, at moderately anemic level: 0.3578, at mildly anemic level: 0.0698, and being non-anemic to be 0.4477. We found that age at marriage (OR=1.13, 95% CI: 1.05, 1.21) and the number of children even born (OR=1.09, 95% CI: 1.03, 1.15) have significant effect on being at or below lower hemoglobin level (severely anemic). Furthermore, age of child (OR=0.92, 95% CI: 0.86-1.00) was a significant predictor, indicating that odds of severe anemia decreases if the child is 48 months or older.
Accelerated Life Testing (ALT) is an effective technique which has been used in different fields ... more Accelerated Life Testing (ALT) is an effective technique which has been used in different fields to obtain more failures in a shorter period of time. It is more economical than traditional reliability testing. In this article, we propose Bayesian inference approach for planning optimal constant stress ALT with Type I censoring. The lifetime of a test unit follows an exponentiated Lomax distribution. Bayes point estimates of the model parameters and credible intervals under uniform and log-normal priors are obtained. Besides, optimum test plan based on constant stress ALT under Type I censoring is developed by minimizing the pre-posterior variance of a specified low percentile of the lifetime distribution at use condition. Gibbs sampling method is used to find the optimal stress with changing time. The performance of the estimation methods is demonstrated for both simulated and real data sets. Results indicate that both the priors and the sample size affect the optimal Bayesian plans. Further, informative priors provide better results than non-informative priors.
In this paper we study bayesian analysis of Modified Weibull distribution under progressively cen... more In this paper we study bayesian analysis of Modified Weibull distribution under progressively censored competing risk model. This study is made for progressively censored data. We use deterministic scan Gibbs sampling combined with slice sampling to generate from the posterior distribution. Posterior distribution is formed by taking prior distribution as reference prior. A real life data analysis is shown for illustrative purpose.
Parametric Confidence Intervals of Spmk for Generalized Exponential Distribution
American Journal of Mathematical and Management Sciences
The objective of this article is to compare highest posterior density (HPD) credible interval wit... more The objective of this article is to compare highest posterior density (HPD) credible interval with three bootstrap confidence intervals (BCIs) as well as with asymptotic confidence interval (ACI) u...
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Papers by Sanku Dey