Bayesian analysis of head and neck cancer data using generalized inverse Lindley stress–strength reliability model

In this article, we present the analysis of head and neck cancer data using generalized inverse Lindley stress–strength reliability model. We propose Bayes estimators for estimating P(X > Y), when X and Y represent survival times of two groups of cancer patients observed under different therapies. The X and Y are assumed to be independent generalized inverse Lindley random variables with common shape parameter. Bayes estimators are obtained under the considerations of symmetric and asymmetric loss functions assuming independent gamma priors. Since posterior becomes complex and does not possess closed form expressions for Bayes estimators, Lindley’s approximation and Markov Chain Monte Carlo techniques are utilized for Bayesian computation. An extensive simulation experiment is carried out to compare the performances of Bayes estimators with the maximum likelihood estimators on the basis of simulated risks. Asymptotic, bootstrap, and Bayesian credible intervals are also computed for the P(X > Y).     

Proportional odds model – a quantile approach

The paper discusses a quantile-based definition for the well-known proportional odds model. We present various reliability properties of the model using quantile functions. Different ageing properties are derived. A generalization for the class of distributions with bilinear hazard quantile function is established and the practical application of this model is illustrated with a real-life data set.     

Short- and long-run rolling causality techniques and optimal window-wise lag selection: an application to the export-led growth hypothesis

The literature devoted to the export-led growth (ELG) hypothesis, which is of utmost importance for policymaking in emerging countries, provides mixed evidence for the validity of the hypothesis. Recent contributions focus on the time-dependence of the relationship between export and output growth using rolling causality techniques based on vector autoregressive models. These models focus on a short-term view which captures single policy-induced developments. However, long-term structural changes cannot be covered by examinations related to the short-term. This paper hence examines the time-varying validity of the ELG hypothesis for India for the period 1960–2011 using rolling causality techniques for both the short-run and long-run horizon. For the first time, window-wise optimal lag-selection procedures are applied in connection with these techniques. We find that exports long-run caused output growth from 1997 until 2009 which can be seen as a consequence of political reforms of the 1990s that boosted economic growth by generating foreign direct investment opportunities and higher exports. For the short-run, export significantly caused output in the period 1998–2003 which followed a concentration of liberalization measures in 1997. Causality in the reversed direction, from output to exports, only seems to be relevant in the short-run.     

Estimating the parameters of a bathtub-shaped distribution under progressive type-II censoring

We consider the problem of estimating unknown parameters, reliability function and hazard function of a two parameter bathtub-shaped distribution on the basis of progressive type-II censored sample. The maximum likelihood estimators and Bayes estimators are derived for two unknown parameters, reliability function and hazard function. The Bayes estimators are obtained against squared error, LINEX and entropy loss functions. Also, using the Lindley approximation method we have obtained approximate Bayes estimators against these loss functions. Some numerical comparisons are made among various proposed estimators in terms of their mean square error values and some specific recommendations are given. Finally, two data sets are analyzed to illustrate the proposed methods.     

Testing equality of conditionally jfclhwdqw exponential distributions

For the models given V = v (a common random stress), X and Y are independently exponentially distributed with failure rates λ₁and λ₂v, testing H₀λ₁λ₂using a random ‘paired’ sample is considered. It is shown that a uniformly most powerful invariant test does not exist even for one sided alternatives; locally most powerful invariant tests are derived and compared with existing procedures. The method is illustrated with reliability data. Finally, the robustness of the tests when the relationships of the failure rates to V is more complex are established.     

Alternative estimators for the population totals in multiple characteristic surveys

The problem of estimating the population totals of multiple characteristics using without replacement sampling design is addressed. The alternative estimators for the study characteristics which are unrelated or have the low correlations with the characteristic used in sample selection are suggested. The efficiency of the estimators under two super population models, approximating the situations in which both the characteristics are unrelated and also when they are related, is studed. A numerical investigation is also carried out to get insight into the performance of the estimators in real applications.     

Modelling lifetimes by quantile functions using Parzen's score function

The present paper introduces methods of constructing quantile functions as models of lifetimes with monotone and nonmonotone hazard functions. This is accomplished on the basis of the relationships the hazard quantile function has with the score function introduced by Parzen in connection with the tail heaviness of probability distributions. Three models illustrated here contain several existing models as particular cases. The appropriateness of the models in real situations is also demonstrated.     

Bayesian Approach to Multicentre Sparse Data

In a 2 × 2 contingency table, when the sample size is small, there may be a number of cells that contain few or no observations, usually referred to as sparse data. In such cases, a common recommendation in the conventional frequentist methods is adding a small constant to every cell of the observed table to find the estimates of the unknown parameters. However, this approach is based on asymptotic properties of the estimates and may work poorly for small samples. An alternative approach would be to use Bayesian methods in order to provide better insight into the problem of sparse data coupled with fewer centers, which would otherwise be difficult to carry out the analysis. In this article, an attempt has been made to use hierarchical Bayesian model to a multicenter data on the effect of a surgical treatment with standard foot care among leprosy patients with posterior tibial nerve damage which is summarized as seven 2 × 2 tables. Monte Carlo Markov Chain (MCMC) techniques are applied in estimating the parameters of interest under sparse data setup.     

Nonparametric repeated significance tests for some analysis of covariance models

For a general class of nonparametric analysis of covariance problems (with stochastic covariates), some repeated significance testing procedures are developed. These procedures rest on the construction of suitable rank order statistics based on the partial sequence of sample sizes and allow for a monitoring of experimentation with the objective of a possible early termination of experimentation. The basic theory is based on the weak convergence of certain stochastic processes relating to the rank order statistics. Various properties of the proposed tests are discussed.