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Measures of stress-strength reliability are most frequently used tools in industrial applications. In multi-component systems, it is of interest to compare stress or strength of individual components with that of the average distribution. For this, recently Gupta et al. [14] have introduced a new stress-strength index (SSI) and obtained some point estimators when underlying populations have exponential distributions. In this paper, we develop bootstrap confidence intervals for SSI and show that they have superior performance as compared to the asymptotic confidence interval based on the maximum likelihood estimator. The results are illustrated by implementation on a real data set. ‘R’ packages have been developed and shared on open source platform for applications by users.

KEYWORDS: Average length; Bayes estimators; Coverage probability; Maximum likelihood estimator; Percentile bootstrap confidence interval; Uniformly minimum variance unbiased estimator

Testing of location parameter is very important and is useful in many fields like agriculture, medical, social, economic etc. When the data does not follow the Normal distribution, the nonparametric tests are more robust and powerful than parametric tests. To address this problem, a new class of test statistic is proposed in this paper which is independent of any distribution. The proposed test is compared with existing nonparametric two sample location tests in the literature, using Pitman and Bahadur asymptotic relative efficiency for some underlying distributions. Optimum choice of sub-sample size is found so that asymptotic relative efficiency is maximized. A real life data example is provided to see the working of the proposed test. A Monte-Carlo simulation study is also applied to find power and level of significance of the proposed test.

KEYWORDS: Nonparametric test; asymptotic relative efficiency; Monte-Carlo simulation

We have, in this paper, developed a sequence of weighted linear regression estimators. The proposed weighted linear regression estimator of order k, besides being endowed with the predictive character, is found to be more efficient than the simple mean estimator in one hand and the weighted linear regression estimator on the other under optimality of k. Based on the theoretical developments, empirical illustrations

involving real-population data have been considered.

KEYWORDS: Hierarchic estimation; predictive estimation; weighted linear regression estimator; bias; mean square error

In a recent paper Sebastian and Gorenflo (2016) introduced Type 2 Generalized Laplacian (T2GL) law and developed the associated AR(1) model after showing that T2GL law belongs to class-L. Here we show that T2GL law is normally attracted to a stable law and it is geometrically infinitely divisible. In fact we prove the results for a T2GL family that contains the T2GL law. We point out the corresponding integervalued T2GL family. Finally, we also clarify a claim in Sebastian and Gorenflo (2016).

KEYWORDS: AR(1) model, ?-decomposable distributions, characteristic function, class-L, discrete stable laws, geometric infinite divisibility, Laplace transform, normal attraction, probability generating function, stable laws

Here we introduce an order k version of the generalized geometric distribution of Kumar and Harisankar (Journal of Statistical Computation and Simulation, 2019) and investigate some of its important properties by deriving an expression for its probability generating function and probability mass function. Certain recurrence relation for its probabilities, raw moments and factorial moments are also obtained, and the maximum likelihood estimation of its parameters is discussed. Certain test

procedures are developed for testing the significance of the additional parameters of the model. All these procedures discussed in the paper are illustrated with the help of real life data sets. A simulation study is also considered for assessing the

performance of the estimators.

KEYWORDS: Generalized geometric Distribution; Generalized Likelihood Ratio Test; Maximum Likelihood Estimation; ; Model Selection: Probability generating function; Simulation