Estimation of the parameter of a dynamically selected population for two subclasses of the exponential family

We introduce the problem of estimation of the parameters of a dynamically selected population in an infinite sequence of random variables and provide its application in the statistical inference based on record values from a non stationary scheme. We develop unbiased estimation of the parameters of the dynamically selected population and evaluate the risk of the estimators. We provide comparisons with natural estimators and obtain asymptotic results. Finally, we illustrate the applicability of the results using real data.     

Is there any polynomial upper bound for the universal labeling of graphs?

A universal labeling of a graph G is a labeling of the edge set in G such that in every orientation \(\ell \) of G for every two adjacent vertices v and u, the sum of incoming edges of v and u in the oriented graph are different from each other. The universal labeling number of a graph G is the minimum number k such that G has universal labeling from \(\{1,2,\ldots , k\}\) denoted it by \(\overrightarrow{\chi _{u}}(G) \). We have \(2\Delta (G)-2 \le \overrightarrow{\chi _{u}} (G)\le 2^{\Delta (G)}\), where \(\Delta (G)\) denotes the maximum degree of G. In this work, we offer a provocative question that is: “Is there any polynomial function f such that for every graph G, \(\overrightarrow{\chi _{u}} (G)\le f(\Delta (G))\)?”. Towards this question, we introduce some lower and upper bounds on their parameter of interest. Also, we prove that for every tree T, \(\overrightarrow{\chi _{u}}(T)={\mathcal {O}}(\Delta ^3) \). Next, we show that for a given 3-regular graph G, the universal labeling number of G is 4 if and only if G belongs to Class 1. Therefore, for a given 3-regular graph G, it is an \( {{\mathbf {N}}}{{\mathbf {P}}} \)-complete to determine whether the universal labeling number of G is 4. Finally, using probabilistic methods, we almost confirm a weaker version of the problem.     

The prevalence of elder abuse and neglect in Iran: a systematic review and meta-analysis

ABSTRACT

Objective: The aim of this study was to estimate the prevalence of elder abuse and neglect in Iran.

Methods: We searched PubMed, Embase, Scopus, and PsycINFO by the end of 2017. The prevalence was calculated based on the percentage or the amount reported in the studies. Heterogeneity was assessed by the I² statistic, and the data were combined using random effects model. The results were reported as the pooled estimates and the 95% confidence intervals (CIs). The review protocol was registered in PROSPERO (CRD42017070744).

Results: A total of 16 studies involving 6,461 participants aged 60 years and over were included. The pooled prevalence for overall elder abuse was 45.7% (95% CI: 27.3–64.1, p < .001).

Discussion: The prevalence of elder abuse and neglect is substantial in the Iranian population aged 60 years and over. More research is needed to investigate the actual prevalence of elder abuse at the national level.     

An analysis of major social obstacles affecting human resource development in Iran

ABSTRACT

This study aimed to analyze the major social obstacles affecting the human resource development (HRD) in Iran. The study population included faculty members in Yazd province, Iran (N = 280, n = 162). A survey and a researcher-made questionnaire were used to collect data. The reliability of the questionnaire was confirmed by using Cronbach’s alpha (0.88) and its validity was approved by a panel of experts. The results indicated that the major social obstacles affecting HRD are ‘an increase in the share of foreigners in the labor market’, ‘frustration of native graduates’ and ‘local brain drain’, respectively. Furthermore, the results of exploratory factor analysis indicated that the most important social obstacles affecting HRD can be summarized into six factors including migration, lack of nativism, inclination towards foreigners, gender imbalance, lack of justice in distribution of resources, and lack of meritocracy. These factors altogether could explain 65.45% of the total variance. In the end, some applied recommendations (such as paying more attention to rural youth, fair distribution of facilities towards urban and rural balance, supporting native elites, preference for employment, and applying indigenous peoples based on meritocracy, creating favorable balance at different levels of academic education, avoiding gender inequality) have been presented.     

Bayesian prediction of minimal repair times of a series system based on hybrid censored sample of components’ lifetimes under Rayleigh distribution

In this paper, we develop Bayesian predictive inferential procedures for prediction of repair times of a series system, applying a minimal repair strategy, using the information contained in an independent observed hybrid censored sample of the lifetimes of the components of the system, assuming the underlying distribution of the lifetimes to be Rayleigh distribution. An illustrative real data example and a simulation study are presented for the purpose of illustration and comparison of the proposed predictors.     

Failure Inference and Optimization for Step Stress Model Based on Bivariate Wiener Model

In this article, we consider the situation under a life test, in which the failure time of the test units are not related deterministically to an observable stochastic time varying covariate. In such a case, the joint distribution of failure time and a marker value would be useful for modeling the step stress life test. The problem of accelerating such an experiment is considered as the main aim of this article. We present a step stress accelerated model based on a bivariate Wiener process with one component as the latent (unobservable) degradation process, which determines the failure times and the other as a marker process, the degradation values of which are recorded at times of failure. Parametric inference based on the proposed model is discussed and the optimization procedure for obtaining the optimal time for changing the stress level is presented. The optimization criterion is to minimize the approximate variance of the maximum likelihood estimator of a percentile of the products’ lifetime distribution.     

Log-gamma-generated families of distributions

We introduce two new general families of continuous distributions, generated by a distribution F and two positive real parameters α and β which control the skewness and tail weight of the distribution. The construction is motivated by the distribution of k-record statistics and can be derived by applying the inverse probability integral transformation to the log-gamma distribution. The introduced families are suitable for modelling the data with a significantly skewed and heavy-tailed distribution. Various properties of the introduced families are studied and a number of estimations and data fitness on real data are given to illustrate the results.     

Fisher Information in Record Values and Their Concomitants: A Comparison of Two Sampling Schemes

Two sampling designs via inverse sampling for generating record data and their concomitants are considered: single sample and multisample. The purpose here is to compare the Fisher information in these two sampling schemes. It is shown that the comparison criterion depends on the underlying distribution. Several general results are established for some parametric families and their well known subclasses such as location-scale and shape families, exponential family and proportional (reversed) hazard model. Farlie-Gumbel-Morgenstern (FGM) family, bivariate normal distribution, and some other common bivariate distributions are considered as examples for illustrations and are classified according to this criterion.     

Comparing Fisher information in record values and their concomitants with random observations

In a sequence of bivariate random variables {(X _i , Y _i ), i≥1} from a continuous distribution with a real parameter θ, general comparison results between the amount of Fisher information about θ contained in the sequence of the first n records and their concomitants, and the desired information in an i.i.d. sample of size n from the parent distribution are established. Some relationships between reliability properties and the proposed criteria are obtained in situations in which the univariate counterpart of the underlying bivariate family belongs to location, scale or shape families. It is also shown that in some classes of bivariate families, the concerned information property is equivalent to that of its univariate counterpart. The proposed procedure is illustrated by considering several examples.