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Showing 21 results for Entropy
Arezoo Habibi Rad, Naser Reza Arghami,
Volume 1, Issue 2 (2-2008)
Abstract
The estimate of entropy (sample entropy), has been introduced by Vasicek (1976), for the first time. In this paper, we provide an estimate of entropy of order statistics, that is the extention of the entropy estimate. Then we present an application of the entropy estimate of order statistics as a test statistic for symmetry of distribution versus skewness. The proposed test has been compared with some other existing tests. A Monte Carlo simulation study shows that the proposed test has more power than the Park's (1999) test.
Ehsan Zamanzadeh, Naser Arghami,
Volume 2, Issue 2 (2-2009)
Abstract
In this paper, we first introduce two new entropy estimators. These estimators are obtained by correcting Corea(1995)'s estimator in the extreme points and also assigning different weights to the end points.We then make a comparison among our proposed new entropy estimators and the entropy estimators proposed by Vasicek (1976), Ebrahimi, et al. (1994) and Corea(1995). We also introduce goodness of fit tests for exponentiality and normality based on our proposed entropy estimators. Results of a simulation study show that the proposed estimators and goodness of fit tests have good performances in comparison with the leading competitors.
Maliheh Abbasnejad, Marzeiyeh Shakouri,
Volume 2, Issue 2 (2-2009)
Abstract
In this paper, we establish a goodness of fit test for exponentiality based on the estimated Renyi information. We use an estimator for Renyi distance in manner of Correa entropy estimate. Critical values of the test are computed by Monte Carlo simulation. Also we compute the power of the test under different alternatives and show that it compares favorably with the leading competitor.
Dr Shahram Mansoury, Dr Eynollah Pasha,
Volume 3, Issue 2 (3-2010)
Abstract
Stochastically ordered random variables with given marginal distributions are combined into a joint distribution preserving the ordering and the marginals using a maximum entropy principle. A closed-form of the maximum entropy density function is obtained. Next we have compared the entropies of maximum entropy distributions, under two constraints The constraints are either prescription of marginal distributions and the marginals and covariance matrix.
Maliheh Abbasnejad Mashhadi, Davood Mohammadi,
Volume 4, Issue 1 (9-2010)
Abstract
In this paper, we characterize symmetric distributions based on Renyi entropy of order statistics in subsamples. A test of symmetry is proposed based on the estimated Renyi entropy. Critical values of the test are computed by Monte Carlo simulation. Also we compute the power of the test under different alternatives and show that it behaves better that the test of Habibi and Arghami (1386).
Eisa Mahmoudi, Reyhaneh Lalehzari,
Volume 5, Issue 1 (9-2011)
Abstract
In this paper a new version of skew uniform distribution is introduced which is completely different from the previous works. Some important properties of the new distribution contain the expression for the density and distribution, kth moments, moment generating and characteristic functions, variance, skewness and kurtusis, mean deviation from the mean, median and mode and parameter estimation are investigated. Also a simulation study on this distribution is carried out to show the consistency of the maximum likelihood and moments estimators. In the end, the new skew uniform distribution is compared with uniform distribution.
Zahra Dastmard, Gholamreza Mohtashami Borzadaran, Bagher Moghaddaszadeh Bazaz,
Volume 5, Issue 2 (2-2012)
Abstract
The class of discrete distributions supported on the setup integers is considered. A discrete version of normal distribution can be characterized via maximum entropy. Also, moments, Shannon entropy and Renyi entropy have obtained for discrete symmetric distribution. It is shown that the special cases of this measures imply the discrete normal and discrete Laplace distributions. Then, an analogue of Fisher information is studied by discrete normal, bilateral power series, symmetric discrete and double logarithmic distributions. Also, the conditions under which the above distributions are unimodal are obtained. Finally, central and non-central moments, entropy and maximum entropy of double logarithmic distribution have achieved.
Ehsan Zamanzade,
Volume 7, Issue 1 (9-2013)
Abstract
In this paper, two new entropy estimators are proposed. Then, entropy-based tests of exponentiality based on our entropy estimators are introduced. Simulation results show that the proposed estimators and related goodness of fit tests have good performances in comparison with their leading competitors.
Bahareh Afhami, Mohsen Madadi, Mohsen Rezapour,
Volume 9, Issue 1 (9-2015)
Abstract
In this paper, first the Shannon entropy of k-record values is derived from the generalized Pareto distribution and propose goodness-of-fit tests based on this entropy. Finally, real data and a simulation study are used for analyzing the performance of this statistic.
Shahram Mansoury,
Volume 9, Issue 1 (9-2015)
Abstract
Jaynes' principle of maximum entropy states that among all the probability distributions satisfying some constraints, one should be selected which has maximum uncertainty. In this paper, we consider the methods of obtaining maximum entropy bivariate density functions via Taneja and Burg's measure of entropy under the constraints that the marginal distributions and correlation coefficient are prescribed. Next, a numerical method is considered. Finally, each method is illustrated via a numerical example.
Fatemeh Hooti, Jafar Ahmadi,
Volume 10, Issue 1 (8-2016)
Abstract
In this paper, the quantile function is recalled and some reliability measures are rewritten in terms of quantile function. Next, quantile based dynamic cumulative residual entropy is obtained and some of its properties are presented. Then, some characterization results of uniform, exponential and Pareto distributions based on quantile based dynamic cumulative entropy are provided. A simple estimator is also proposed and its performance is studied for exponential distribution. Finally discussion and results are presented.
Nader Nematollahi,
Volume 10, Issue 2 (2-2017)
Abstract
In some applied problems we need to choose a population from the given populations and estimate the parameter of the selected population. Suppose k random samples are chosen from k populations with proportional hazard rate model or proportional reversed hazard rate model. According to a specified selection rule, it is desired to estimate the parameter of the best (worst) selected population. In this paper, under the entropy loss function we obtain the uniformly minimum risk unbiased (UMRU) estimator of the parameters of the selected population, and derived sufficient conditions for minimaxity of a given estimator. Then we find the class of admissible and inadmissible linear estimators of the parameters of the selected population and determine the class of dominators of a given estimator. We show that the UMRU estimator is inadmissible and compare the obtained estimators by plotting their risk functions.
Mrs Manije Sanei Tabass, Professor Gholamreza Mohtashami Borzadaran,
Volume 11, Issue 1 (9-2017)
Abstract
Maximum of the Renyi entropy and the Tsallis entropy are generalization of the maximum entropy for a larger class of Shannon entropy. In this paper we introduce the maximum Renyi entropy and some of the attributes of distributions which have maximum Renyi entropy investigated. The form of distributions with maximum Renyi entropy is power so we state some properties of these distributions and we have a new form of the Renyi entropy. After pointing the topics of minimum Renyi divergence, some other points in this relation have been discussed. An another form of Renyi divergence have also obtained. Therefore we discussed some of the economic applications of the maximum entropy. Meanwhile, the review of the Csiszar information measure, the general form of distributions with minimum Renyi divergence have obtained.
Afsaneh Shokrani, Mohammad Khorashadizadeh,
Volume 12, Issue 2 (3-2019)
Abstract
This paper first introduces the Kerridge inaccuracy measure as an extension of the Shannon entropy and then the measure of past inaccuracy has been rewritten based on the concept of quantile function. Then, some characterizations results for lifetimes with proportional reversed hazard model property based on quantile past inaccuracy measure are obtained. Also, the class of lifetimes with increasing (decreasing) quantile past inaccuracy property and some of its properties are studied. In addition, via an example of real data, the application of quantile inaccuracy measure is illustrated.
Vahideh Ahrari, Simindokht Baratpour, Arezo Habibirad,
Volume 12, Issue 2 (3-2019)
Abstract
Entropy plays a fundamental role in reliability and system lifetesting areas. In the recent studies, much attentions have been paid to use quantile functions properties and their applications as an alternate approac in distinguishing statistical models and analysis of data. In the present paper, quantile based residual Tsallis entropy is introduced and its properties in continuous models are investigated. Considering distributions of certain lifetime, explicit versions for quantile based residual Tsallis entropy are obtained and their properties monotonicity are studied and characterization based on this entropy is investigated. Also quantile based Tsallis divergence is introduced and quantile based residual Tsallis divergence is obtained. Finally, an estimator for the quantile based residual Tsallis entropy is introduced and its performance is investigate by study simulation.
Atefe Pourkazemi, Hadi Alizadeh Noughabi, Sara Jomhoori,
Volume 13, Issue 2 (2-2020)
Abstract
In this paper, the Bootstrap and Jackknife methods are stated and using these methods, entropy is estimated. Then the estimators based on Bootstrap and Jackknife are investigated in terms of bias and RMSE using simulation. The proposed estimators are compared with other entropy estimators by Monte Carlo simulation. Results show that the entropy estimators based on Bootstrap and Jackknife have a good performance as compared to the other estimators. Next, some tests of normality based on the proposed estimators are introduced and the power of these tests are compared with other tests.
Seyede Toktam Hosseini, Jafar Ahmadi,
Volume 14, Issue 2 (2-2021)
Abstract
In this paper, using the idea of inaccuracy measure in the information theory, the residual and past inaccuracy measures in the bivariate case are defined based on copula functions. Under the assumption of radial symmetry, the equality of these two criteria is shown, also by the equality between these two criteria, radially symmetrical models are characterized. A useful bound is provided by establishing proportional (inverse) hazard rate models for marginal distributions. Also, the proportional hazard rate model in bivariate mode is characterized by assuming proportionality between the introduced inaccuracy and its corresponding entropy. In addition, orthant orders are used to obtain inequalities. To illustrate the results, some examples and simulations are presented.
Anis Iranmanesh, Farzaneh Oliazadeh, Vahid Fakoor,
Volume 15, Issue 2 (3-2022)
Abstract
In this article, we propose two non-parametric estimators for the past entropy based on length-biased data, and the strong consistency of the proposed estimators is proved. In addition, some simulations are conducted to evaluate the performance of the proposed estimators. Based on the results, we show that they have better performance in a different region of the probability distribution for length-biased random variables.
Dr Alireza Chaji,
Volume 16, Issue 2 (3-2023)
Abstract
High interpretability and ease of understanding decision trees have made
them one of the most widely used machine learning algorithms. The key to building
efficient and effective decision trees is to use the suitable splitting method. This
paper proposes a new splitting approach to produce a tree based on the T-entropy criterion
for the splitting method. The method presented on three data sets is examined
by 11 evaluation criteria. The results show that the introduced method in making
the decision tree has a more accurate performance than the well-known methods of
Gini index, Shannon, Tisalis, and Renny entropies and can be used as an alternative
method in producing the decision tree.
Shahrastani Shahram Yaghoobzadeh,
Volume 17, Issue 1 (9-2023)
Abstract
In this article, it is assumed that the arrival rate of customers to the queuing system M/M/c has an exponential distribution with parameter $lambda$ and the service rate of customers has an exponential distribution with parameter $mu$ and is independent of the arrive rate. It is also assumed that the system is active until time T. Under this stopping time, maximum likelihood estimation and bayesian estimation under general entropy loss functions and weighted error square, as well as under-informed and uninformed prior distributions, the system traffic intensity parameter M/M/c and system stationarity probability are obtained. Then the obtained estimators are compared by Monte Carlo simulation and a numerical example to determine the most suitable estimator.
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