Generalized exponential distribution: Moments of order statistics

In this paper, we consider the generalized exponential distribution (GED) with shape parameter α. We establish several recurrence relations satisfied by the single and the product moments for order statistics from the GED. The relationships can be written in terms of polygamma and hypergeometric functions and used in a simple recursive manner in order to compute the single and the product moments of all order statistics for all sample sizes.     

Some results on the mean residual waiting time of records

Often, in reliability theory, risk analysis, renewal processes and actuarial studies, mean residual life function or life expectancy plays an important role in studying the conditional tail measure of lifetime data. In this paper, we introduce the notion of the mean residual waiting time of records and present some monotonic and aging properties. Sharp bounds for the mean residual waiting time of records are also investigated.     

On the efficiency of monte carlo methods using steady state ranked simulated samples

Samawi (1999) showed that the efficiency of Monte Carlo methods of integrals estimation can be substantially improved by using ranked simulated samples (RSIS) in place of uniform simulated samples (USIS). However, in this paper it is shown that substantial improvement of efficiency can be achieved further by using the steady state ranked simulated sample (SRSIS). It appears that the modified Monte Carlo methods using SRSIS provide unbiased and more efficient estimators for the integrals. Some theoretical properties of SRSIS are given. A simulation study is conducted to compare the performance of the methods using SRSIS with respect to USIS, for some examples.     

A note on Pitman's measure of closeness with balanced loss function

In this note, we consider the problem of estimating an unknown parameter θ in the sense of the Pitman's measure of closeness (PMC) using the balanced loss function (BLF). We show that the PMC comparison of estimators under the BLF can be reduced to the PMC comparison under the usual absolute error loss. The Pitman-closest estimators of the location and scale parameters under BLF are also characterized. Illustrative examples are given to show the broad range applications of the obtained results.     

The origin of semilingualism: Nils-Erik Hansegård and the cult of the mother tongue

‘Semilingualism’ is one of the most questionable theories produced in the language sciences. Yet, little is known about its origins. We present a critical account of the history of semilingualism, tracing its roots in the work of Nils Erik Hansegård, (1918–2002), inaugural chair of Sámi at Umeå University (1975–1979), who developed a theory of semilingualism (halvspråkighet) in the 1960s. We show how Hansegård theorized semilingualism using ideas from Nazi German linguistics, producing an unforgiving theory of linguistic pathology directed at minoritized bilinguals in Sweden's far north.     

Inference for the generalized Rayleigh distribution based on progressively censored data

In this paper, and based on a progressive type-II censored sample from the generalized Rayleigh (GR) distribution, we consider the problem of estimating the model parameters and predicting the unobserved removed data. Maximum likelihood and Bayesian approaches are used to estimate the scale and shape parameters. The Gibbs and Metropolis samplers are used to predict the life lengths of the removed units in multiple stages of the progressively censored sample. Artificial and real data analyses have been performed for illustrative purposes.     

A generalization of Turnbull’s estimator for nonparametric estimation of the conditional survival function with interval-censored data

Simple nonparametric estimates of the conditional distribution of a response variable given a covariate are often useful for data exploration purposes or to help with the specification or validation of a parametric or semi-parametric regression model. In this paper we propose such an estimator in the case where the response variable is interval-censored and the covariate is continuous. Our approach consists in adding weights that depend on the covariate value in the self-consistency equation proposed by Turnbull (J R Stat Soc Ser B 38:290–295, 1976), which results in an estimator that is no more difficult to implement than Turnbull’s estimator itself. We show the convergence of our algorithm and that our estimator reduces to the generalized Kaplan–Meier estimator (Beran, Nonparametric regression with randomly censored survival data, 1981) when the data are either complete or right-censored. We demonstrate by simulation that the estimator, bootstrap variance estimation and bandwidth selection (by rule of thumb or cross-validation) all perform well in finite samples. We illustrate the method by applying it to a dataset from a study on the incidence of HIV in a group of female sex workers from Kinshasa.     

Bayesian classification with multivariate autoregressive sources that might have different orders

The main objective of this paper is to develop an exact Bayesian technique that can be used to assign a multivariate time series realization to one of several autoregressive sources, with unknown coefficients and precision, that might have different orders. The foundation of the proposed technique is to develop the posterior mass function of a classification vector, in an easy form, using the conditional likelihood function. A multivariate time series realization is assigned to the multivariate autoregressive source with the largest posterior probability. A simulation study, with uniform prior mass function, is carried out to demonstrate the performance of the proposed technique and to test its adequacy in handling the multivariate classification problems. The analysis of the numerical results supports the adequacy of the proposed technique in solving the classification problems with multivariate autoregressive sources.     

Improved attribute acceptance sampling plans based on maxima nomination sampling

This paper demonstrates the use of maxima nomination sampling (MNS) technique in design and evaluation of single AQL, LTPD, and EQL acceptance sampling plans for attributes. We exploit the effect of sample size and acceptance number on the performance of our proposed MNS plans using operating characteristic (OC) curve. Among other results, we show that MNS acceptance sampling plans with smaller sample size and bigger acceptance number perform better than commonly used acceptance sampling plans for attributes based on simple random sampling (SRS) technique. Indeed, MNS acceptance sampling plans result in OC curves which, compared to their SRS counterparts, are much closer to the ideal OC curve. A computer program is designed which can be used to specify the optimum MNS acceptance sampling plan and to show, visually, how the shape of the OC curve changes when parameters of the acceptance sampling plan vary. Theoretical results and numerical evaluations are given.