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The skew normal (SN) distribution of Azzalini (Scand J Stat 12:171–178, 1985) is one of the widely used probability distributions for modelling skewed data. In this article, we introduce a general class of skewed distributions based on mean mixtures of normal distributions, which includes the SN distribution as a special case. Some properties of this new class, such as expressions for mean, variance,...
In this paper, we address the problem of deciding if either n consecutive independent failure times have the same failure rate or if there exists some $$k\in \{1,\ldots ,n\}$$ k ∈ { 1 , … , n } such that the common failure rate of the first k failure times is different from the common failure rate of the last $$n-k$$ n - k failure times, based on an exponential lifetime distribution...
The objective of this paper is to study the issue of the generalized projection discrepancy along the line of Qin et al. (J Stat Plan Inference 142:1170–1177, 2012) based on generalized discrete discrepancy measure proposed by Chatterjee and Qin (J Stat Plan Inference 141:951–960, 2011). We shall study the projection properties for general asymmetric factorials and provide some analytic connections...
We study here extremes of residuals of the bivariate lifetime and the residual of extremes of the two lifetimes. In the case of generalized Marshall–Olkin model and the total time transformed exponential model, we first present some sufficient conditions for the extremes of residuals to be stochastically larger than the residual of the corresponding extremes, and then investigate the stochastic order...
In this paper, we discuss the statistical inference of the lifetime distribution of components based on observing the system lifetimes when the system structure is known. A general proportional hazard rate model for the lifetime of the components is considered, which includes some commonly used lifetime distributions. Different estimation methods—method of moments, maximum likelihood method and least...
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