In this short note, we focus on the limiting behaviors of moments for normalized partial maxima of skew-normal samples. Under optimal norming constants, asymptotic expansions for moments of maxima of skew-normal samples are derived. These expansions are used to deduce convergence rates of...

In this paper, we consider the missing information in determining the optimal allocation of removals in a Type II progressive censoring scheme. We provide a simple expression and a recurrence relation for the missing information. Then we provide a simple way of determining an optimal censoring...

For a skew-normal random sequence, convergence rates of the distribution of its partial maximum to the Gumbel extreme value distribution are derived. The asymptotic expansion of the distribution of the normalized maximum is given under an optimal choice of norming constants. We find that the...

In this paper, we derive the exact uniform convergence rate of the asymmetric normal distribution of the maximum and minimum to its extreme value limit.

This paper considers the maximum deviation of the error density estimator in linear regression with right censored data. Based on the Kaplan–Meier estimator of the residual distribution, we define the kernel-smoothed estimator of an error density function. The limit distributions for the...

Lindsay (1994) provided a general set up in discrete models for minimum disparity estimation. Such a set up eludes us in continuous models. We provide such a general result and hence fill up a major gap in the literature.

The Birnbaum–Saunders distribution is based on the asymptotic normality of a sum of random variables. We propose a new version of this distribution assuming that the number of terms of such a sum depends on a non-homogeneous Poisson process. The classical Birnbaum–Saunders distribution is...

According to the δ-shock model, the system fails when the time between two consecutive shocks falls below a fixed threshold δ. This model has a potential application in various fields such as inventory, insurance and system reliability. In this paper, we study run-related generalization of...

In this paper, the Pitman’s measure of closeness of current k-records to the population quantiles is investigated. While the required probabilities typically depend on the underlying distribution, in this article, we show that they are distribution-free for the symmetric distributions. The...