Non-parametric prediction intervals for the lifetime of coherent systems

In this paper, nonparametric methods are proposed to construct prediction intervals for the lifetime of a coherent system with known signatures. An explicit expression for the coverage probability of the prediction intervals is presented based on Samaniego’s signature. The existence and optimality of these intervals are discussed. In our derivation, we also obtain an exact expression for the marginal distribution of the \(i\) th order statistic from a pooled sample.     

Identity Crisis and Integration: The Divergent Attitudes of Iranian Immigrant Men and Women towards Integration into Swedish Society

The main objective of this article is to show the divergent attitudes of Iranian immigrant men and women towards integration into Swedish society.
As several studies have shown, Iranian women have a better chance of adjusting to Western societies than Iranian men. This article discusses the notion that one of the important reasons for this is the determining role of professional position in the life of Iranian immigrants in Sweden.
As a result of the improvement in their work status and therefore an improvement in their social position, Iranian immigrant women now have greater possibilities than Iranian immigrant men to overcome the identity crisis which ordinarily makes ethnic groups and cultural minorities lose their sense of fitting into their new social reality.
This results, in its turn, in the women having a positive attitude towards the new society and increases the extent of their desire for integration into the new society.     

On the Nearness of Records to Population Quantiles with Respect to Order Statistics in the Sense of Pitman Closeness

In this paper, Pitman closeness criterion is used to compare the nearness of record values and order statistics from two independent samples to a specific population quantile of the parent distribution while the underlying distributions are the same. General expressions for the associated Pitman closeness probability are obtained when the support of the parent distribution is bounded and also unbounded. Some distribution-free results are achieved for symmetric distributions. The exponential and uniform distributions are considered for illustrative proposes and exact expressions are obtained in each case.     

Characterizations based on Rényi entropy of order statistics and record values

Two different distributions may have equal Rényi entropy; thus a distribution cannot be identified by its Rényi entropy. In this paper, we explore properties of the Rényi entropy of order statistics. Several characterizations are established based on the Rényi entropy of order statistics and record values. These include characterizations of a distribution on the basis of the differences between Rényi entropies of sequences of order statistics and the parent distribution.     

Point estimation of lower quantiles based on two-sampling scheme

ABSTRACT

Consider a two-sampling scheme in which an initial sample is first taken from the underlying population and then by assuming a suitable restriction on this sample, some more data points are observed as a new restricted sample. This sampling scheme is used to do inference about the lower quantiles of the underlying distribution. The results are compared with those of simple random sampling in view of mean squared error and Pitman’s measure of closeness criteria for exponential and uniform distributions. It will be shown that the proposed sampling scheme would improve the performance of the point estimators of the lower quantiles of the population.     

Confidence and prediction intervals based on interpolated records

In several statistical problems, nonparametric confidence intervals for population quantiles can be constructed and their coverage probabilities can be computed exactly, but cannot in general be rendered equal to a pre-determined level. The same difficulty arises for coverage probabilities of nonparametric prediction intervals for future observations. One solution to this difficulty is to interpolate between intervals which have the closest coverage probability from above and below to the pre-determined level. In this paper, confidence intervals for population quantiles are constructed based on interpolated upper and lower records. Subsequently, prediction intervals are obtained for future upper records based on interpolated upper records. Additionally, we derive upper bounds for the coverage error of these confidence and prediction intervals. Finally, our results are applied to some real data sets. Also, a comparison via a simulation study is done with similar classical intervals obtained before.     

Entropy properties of record statistics

Record values can be viewed as order statistics from a sample whose size is determined by the values and the order of occurrence of observations. They are closely connected with the occurrence times of a corresponding non-homogenous Poisson process and reliability theory. In this paper, the information properties of record values are presented based on Shannon information. Several upper and lower bounds for the entropy of record values are obtained. It is shown that, the mutual information between record values is distribution free and is computable using the distribution of the record values of the sequence from the uniform distribution.     

Estimation for the Parameters of Generalized Half-normal Distribution Based on Progressive Type-I Interval Censoring

Based on progressively Type-I interval censored sample, the problem of estimating unknown parameters of a two parameter generalized half-normal(GHN) distribution is considered. Different methods of estimation are discussed. They include the maximum likelihood estimation, midpoint approximation method, approximate maximum likelihood estimation, method of moments, and estimation based on probability plot. Several Bayesian estimates with respect to different symmetric and asymmetric loss functions such as squared error, LINEX, and general entropy is calculated. The Lindley’s approximation method is applied to determine Bayesian estimates. Monte Carlo simulations are performed to compare the performances of the different methods. Finally, analysis is also carried out for a real dataset.     

Lifetime performance index based on ranked set sampling

In this article, we assume that the lifetimes of products follow a one-parameter exponential distribution and use both conjugate and Jeffreys prior distributions for finding a Bayes estimator based on the RSS scheme for lifetime performance index CL. We also obtained maximum likelihood and adhac estimators for CL. Monte Carlo simulation study is done for comparing the obtained estimators in two sampling schemes SRS and RSS. Fisher information has been utilized to obtain lower confidence bound of CL for both schemes in asymptotically state and use this bounds for hypothesis testing of CL.