In this paper we propose an estimator of the entropy of a continuous random variable. The estimator is obtained by modifying the estimator proposed by Vasicek (1976). Consistency of estimator is proved, and comparisons are made with Vasicek’s estimator (1976), van Es’s estimator (1992), Ebrahimi et al.’s estimator (1994) and Correa’s estimator (1995). The results indicate that the proposed estimator has smaller mean squared error than above estimators.

In this article, we introduce a new estimator of entropy of continuous random variable. Bias, variance and the mean squared error of the new estimator are obtained and compared with the other existing estimators. The results show that the proposed estimator has a lower mean squared error than its competitors. Then, we propose some goodness of fit tests for Weibull distribution based on the entropy estimators. To assess the effectiveness of the proposed tests, we utilize Monte Carlo simulation to evaluate their power against eighteen different alternatives with varying sample sizes. The results show that the tests are powerful and we can use them in practice. Finally, two real datasets are considered and modeled by the Weibull distribution.

The traditional method for studying non-stationary signals is spectrogram based on the short-time Fourier transform (STFT). The well known limitation of the STFT is the inherent trade-off between time and frequency resolution. The Wigner-Ville (WV) distribution has the best time-frequency resolution, but its draw back is generating cross-terms. The matching pursuit (MP) distribution based on using the Gaussian atom is always positive, does not include crossterm, and has convenient resolution. In this paper, we have shown in addition to the known properties, the MP distribution can also remove the additive noise inherently. On the other words, we are able to remove the noise just by limiting the algorithm iterations and without paying any additional cost. Although the MP distribution based on using the Gaussian atoms is always positive and it has convenient resolution, according to the MP the time marginal and the frequency marginal will not be obtained accurately. In this paper, it has been shown that by implementing the minimum cross entropy (MCE) technique according to the MP distribution as a priory positive distribution, the new extracted distribution has the most similarity to the MP distribution and it also satisfies the correct time and frequency marginal.

Our main objective in this paper is to analyze Bayesian Shrinkage Estimators of the parameter of two-parameter Exponential Distribution Scale under General Entropy Loss Function based on the prior conjugate distribution and Progressive Type-II Censored Data in the presence of the location parameter. To this end, in the present paper, firstly, we present Shrinkage Estimator of scale parameter based on the Bayesian estimator that obtained under General Entropy Loss Function, and prior conjugate distribution, and then investigate the efficiency of the proposed estimator with other estimators, such as maximum likelihood estimator, Bayes estimator, empirical Bayesian estimator, and empirical Bayesian Shrinkage Estimator. The method used in this paper to compute empirical Bayesian estimator, and empirical Bayesian Shrinkage Estimator is guessing. Using simulated data based on Monte Carlos’ method, under six censorship schemes and with two prior distributions of Jeffrey and Hartigan, the effectiveness of estimators is compared. Finally, using actual data, the efficiency of the proposed estimators will be examined.

In this paper, we show that the unbiased estimator of the certion Parameter of the selected population does not exist. First, we give a new proof of this fact for the selected normal population. We then extend the result to some other distributions belonging to one-parameteric exponential family. Whenever an unbiased estimator exists, it is shown to be a function of order statiscs.

Due to the lack of measurement in distribution systems, state estimation has particular importance. Different methods are presented to improve the accuracy of system state with limited measurements. In this paper a new state estimator in distribution systems are offered. This estimator bases on backward forward load flow estimates system state with adjusting load consumption at each step. Voltage measurements in slack bus, loads and zero injection measurements are inputs of estimator. This estimator is compared with weight least square estimator and its results are shown. The estimator calculates voltage magnitude with less error and also faster than WLS estimator. 85-bus system is presented in this paper.

The purpose of this study is to define the concepts of Tsallis entropy and conditional Tsallis entropy of fuzzy partitions and to obtain some results concerning this kind entropy. We show that the Tsallis entropy of fuzzy partitions has the subadditivity and concavity properties. We study this information measure under the refinement and zero mode subset relations. We check the chain rules for this information measure and prove some properties about the entropy of independent fuzzy partitions. Some results of the relationship between the Tsallis entropy and conditional Tsallis entropy of fuzzy partitions are obtained and, by using conditional Tsallis entropy of fuzzy partitions, we show that the subadditivity property for Tsallis entropy of fuzzy partitions is not established in the case that the parameter of this entropy is smaller than one. In general, the Tsallis entropy of fuzzy partitions has similar properties to the shannon entropy, where the parameter of this entropy is larger than one, and therefore can be used in addition to the Shannon entropy, to measure the amount of information to be extracted from a fuzzy experiment.

We propose a nonparametric estimator for the residual entropy function based on length-biased data. Some asymptotic results have been proved. The strong consistency and asymptotic normality of the proposed estimator are established under suitable regularity conditions. Monte Carlo simulation studies are carried out to evaluate the performance of the estimator using the bias and mean-squared error. A real data set is considered, and we show that the data follow a length-biased distribution. Moreover, the proposed estimator yields a better value for the estimated residual entropy in comparison to the competitor estimator.

We introduce a goodness of fit test for exponentiality based on record values. The critical points and powers for some alternatives are obtained by simulation.