An efficient and fast algorithm for estimating the parameters of two-dimensional sinusoidal signals

In this paper we propose a computationally efficient algorithm to estimate the parameters of a 2-D sinusoidal model in the presence of stationary noise. The estimators obtained by the proposed algorithm are consistent and asymptotically equivalent to the least squares estimators. Monte Carlo simulations are performed for different sample sizes and it is observed that the performances of the proposed method are quite satisfactory and they are equivalent to the least squares estimators. The main advantage of the proposed method is that the estimators can be obtained using only finite number of iterations. In fact it is shown that starting from the average of periodogram estimators, the proposed algorithm converges in three steps only. One synthesized texture data and one original texture data have been analyzed using the proposed algorithm for illustrative purpose.     

Women's political leadership participation around the world: An institutional analysis

Understanding institutional systems is critical for the advancement of women's participation in leadership in varying contexts. A unique and global analysis of the contextual factors that affect women in political leadership, this paper extends prior research in the field. This is a cross-country study where we ask, “How are societal-level institutional forces related to women's participation in political leadership?” We collected data from 8 secondary sources on 181 countries and conducted linear regression analyses with six institutional influences: the business environment, societal development, the economic environment, physical and technological infrastructure, political freedom, and culture. Results indicate that to increase the political leadership participation of women, we need to evaluate the following: customs and trade regulations, graft, the gender gap in political empowerment, public spending on education, the economic viability of the country, access to power and the internet, political freedom, and cultural variables like performance orientation, collectivism, and power distance.     

Some distributional results through past entropy

Measure of uncertainty in past lifetime distribution plays an important role in the context of Information Theory, Forensic Science and other related fields. In this paper we provide characterizations of quite a few continuous and discrete distributions based on certain functional relationships among past entropy, reversed hazard rate and expected inactivity time. Based on past entropy, a conditional measure of uncertainty has been defined, which has helped in defining a new stochastic order and an ageing class. The properties of the stochastic order and those of the ageing class are also studied here.     

Exact inference for the two-parameter exponential distribution under Type-II hybrid censoring

Epstein (1954) introduced the Type-I hybrid censoring scheme as a mixture of Type-I and Type-II censoring schemes. Childs et al. (2003) introduced the Type-II hybrid censoring scheme as an alternative to Type-I hybrid censoring scheme, and provided the exact distribution of the maximum likelihood estimator of the mean of a one-parameter exponential distribution based on Type-II hybrid censored samples. The associated confidence interval also has been provided. The main aim of this paper is to consider a two-parameter exponential distribution, and to derive the exact distribution of the maximum likelihood estimators of the unknown parameters based on Type-II hybrid censored samples. The marginal distributions and the exact confidence intervals are also provided. The results can be used to derive the exact distribution of the maximum likelihood estimator of the percentile point, and to construct the associated confidence interval. Different methods are compared using extensive simulations and one data analysis has been performed for illustrative purposes.     

On study of dynamic survival and cumulative past entropies

Abstract

Recently, a new class of measure of uncertainty, called “dynamic survival entropy”, has been defined and studied in the literature. Based on this entropy, DSE(α) ordering, IDSE(α), and DDSE(α) classes of life distributions are defined and some results are studied. In this paper, our main aim is to prove some more results of the ordering and the aging classes of life distributions mentioned above. Some important distributions such as exponential, Pareto, Pareto II, and finite range distributions are also characterized. Here we have defined cumulative past entropy and proved some interesting results.     

Bayesian Analysis of Different Hybrid and Progressive Life Tests

Type-I and Type-II censoring schemes are the widely used censoring schemes available for life testing experiments. A mixture of Type-I and Type-II censoring schemes is known as a hybrid censoring scheme. Different hybrid censoring schemes have been introduced in recent years. In the last few years, a progressive censoring scheme has also received considerable attention. In this article, we mainly consider the Bayesian inference of the unknown parameters of two-parameter exponential distribution under different hybrid and progressive censoring schemes. It is observed that in general the Bayes estimate and the associated credible interval of any function of the unknown parameters, cannot be obtained in explicit form. We propose to use the Monte Carlo sampling procedure to compute the Bayes estimate and also to construct the associated credible interval. Monte Carlo Simulation experiments have been performed to see the effectiveness of the proposed method in case of Type-I hybrid censored samples. The performances are quite satisfactory. One data analysis has been performed for illustrative purposes.     

Analysis of middle-censored data with exponential lifetime distributions

Recently Jammalamadaka and Mangalam [2003. Non-parametric estimation for middle censored data. J. Nonparametric Statist. 15, 253–265] introduced a general censoring scheme called the “middle-censoring” scheme in non-parametric set up. In this paper we consider this middle-censoring scheme when the lifetime distribution of the items is exponentially distributed and the censoring mechanism is independent and non-informative. In this set up, we derive the maximum likelihood estimator and study its consistency and asymptotic normality properties. We also derive the Bayes estimate of the exponential parameter under a gamma prior. Since a theoretical construction of the credible interval becomes quite difficult, we propose and implement Gibbs sampling technique to construct the credible intervals. Monte Carlo simulations are performed to evaluate the small sample behavior of the techniques proposed. A real data set is analyzed to illustrate the practical application of the proposed methods.     

Discriminating among Weibull,log-normal,and log-logistic distributions

In this article, we consider the problem of the model selection/discrimination among three different positively skewed lifetime distributions. All these three distributions, namely; the Weibull, log-normal, and log-logistic, have been used quite effectively to analyze positively skewed lifetime data. In this article, we have used three different methods to discriminate among these three distributions. We have used the maximized likelihood method to choose the correct model and computed the asymptotic probability of correct selection. We have further obtained the Fisher information matrices of these three different distributions and compare them for complete and censored observations. These measures can be used to discriminate among these three distributions. We have also proposed to use the Kolmogorov–Smirnov distance to choose the correct model. Extensive simulations have been performed to compare the performances of the three different methods. It is observed that each method performs better than the other two for some distributions and for certain range of parameters. Further, the loss of information due to censoring are compared for these three distributions. The analysis of a real dataset has been performed for illustrative purposes.