Vikas Kumar Sharma

The inverse Lindley distribution: a stress-strength reliability model with application to head and neck cancer data

In this article, we proposed one parameter, inverse Lindley distribution, with its fundamental properties such as quantiles, mode, stochastic ordering, entropy, and stress–strength reliability. The proposed distribution has upside-down bathtub shape for its failure rate function. The estimation of stress–strength reliability has been approached by both classical and Bayesian methods. Under Bayesian set-up, both non-informative (Jeffrey) and informative (gamma) priors are considered under symmetric (squared error) and asymmetric (entropy) loss functions. The Lindley’s approximation method is used for Bayesian computation. The performances of the estimators have been compared in terms of their mean squared errors using simulated samples. Two real data-sets, representing the survival times of head and neck cancer patients, are considered for demonstrating the applicability of the proposed model.

Heterocyclic Chalcone Analogues as Potential Anticancer Agents

Chalcones, aromatic ketones and enones acting as the precursor for flavonoids such as Quercetin, are known for their anticancer effects. Although, parent chalcones consist of two aromatic rings joined by a three-carbon α,β-unsaturated carbonyl system, various synthetic compounds possessing heterocyclic rings like pyrazole, indole etc. are well known and proved to be effective anticancer agents. In addition to their use as anticancer agents in cancer cell lines, heterocyclic analogues are reported to be effective even against resistant cell lines. In this connection, we hereby highlight the potential of various heterocyclic chalcone analogues as anticancer agents with a brief summary about therapeutic potential of chalcones, mechanism of anticancer action of various chalcone analogues, and current and future prospects related to the chalcones-derived anticancer research. Furthermore, some key points regarding chalcone analogues have been reviewed by analyzing their medicinal properties.

A new upside-down bathtub shaped hazard rate model for survival data analysis

Abstract 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.

The Generalized Inverse Lindley Distribution: A New Inverse Statistical Model for the Study of Upside-down Bathtub Data

ABSTRACT In this article, a two-parameter generalized inverse Lindley distribution capable of modeling a upside-down bathtub-shaped hazard rate function is introduced. Some statistical properties of proposed distribution are explicitly derived here. The method of maximum likelihood, least square, and maximum product spacings are used for estimating the unknown model parameters and also compared through the simulation study. The approximate confidence intervals, based on a normal and a log-normal approximation, are also computed. Two algorithms are proposed for generating a random sample from the proposed distribution. A real data set is modeled to illustrate its applicability, and it is shown that our distribution fits much better than some other existing inverse distributions.

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

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.

The Beta-Lindley Distribution: Properties and Applications

We introduce the new continuous distribution, the so-called beta-Lindley distribution that extends the Lindley distribution. We provide a comprehensive mathematical treatment of this distribution. We derive the moment generating function and the rth moment thus, generalizing some results in the literature. Expressions for the density, moment generating function, and rth moment of the order statistics also are obtained. Further, we also discuss estimation of the unknown model parameters in both classical and Bayesian setup. The usefulness of the new model is illustrated by means of two real data sets. We hope that the new distribution proposed here will serve as an alternative model to other models available in the literature for modelling positive real data in many areas.

Bayesian Estimation and Prediction for Flexible Weibull Model under Type-II Censoring Scheme

We have developed the Bayesian estimation procedure for flexible Weibull distribution under Type-II censoring scheme assuming Jeffreys 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.

Enhanced efficacy and a better pharmacokinetic profile of tamoxifen employing polymeric micelles

The present work aims to develop tamoxifen-loaded polymeric micelles and explore their potential in topical delivery of the drug to breast cancer cells. The PLGA–PEG copolymer was chemically synthesized and the critical micelle concentration (CMC) of the polymer was determined, drug loaded micelles were developed by a modified solvent dialysis method. The developed system was characterized for micromeritics, surface charge, drug entrapment and morphology. Furthermore, nanocarriers were evaluated for drug-release-kinetics, erythrocyte-compatibility, in vitro cytotoxicity against MCF-7 breast cancer cells and a dermal pharmacokinetic profile. The developed system was of a spherical shape with size of 76.4 ± 2.1 nm and a neutral surface charge (−4.89 mV). The system was able to offer 60.86 ± 3.21% drug entrapment. Along with drug release controlling behaviour, the cytotoxic potential of tamoxifen against MCF-7 cell lines was substantially enhanced. Dermatokinetic studies revealed better drug availability to both the epidermis and dermis than that of the plain drug. The PLGA–PEG-based micellar system offered a safer and effective option for better delivery of tamoxifen to breast cancer with immense promise of delivery across skin.

Bayesian analysis for Type-II hybrid censored sample from inverse Weibull distribution

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.

Estimation and prediction for Type-I hybrid censored data from generalized Lindley distribution

Abstract This paper consider the problems of estimation and prediction using Type-I hybrid censored lifetime data that follow generalized Lindley distribution. Maximum likelihood estimators as well as Bayes estimators have been proposed for estimating the parameters and reliability characteristics from the generalized Lindley distribution. Since posteriors are not in closed forms, Markov Chain Monte Carlo techniques such as Gibbs sampler and Metropolis-Hastings algorithm have been utilized to explore the properties of the posteriors. Monte Carlo simulation study has been carried out to compare the classical and Bayesian estimation methods. One and two sample predictive posteriors of future order statistics are also derived on the basis of Type-I hybrid censored data. Finally, a set of real data is analysed for illustration.