فهرست مطالب gholamreza mohtashami borzadaran

Maximum entropy copula theory is a combination of copula and entropy theory. This method obtains the maximum entropy distribution of random variables by considering the dependence structure. In this paper, the most entropic copula based on Blest's measure is introduced, and its parameter estimation method is investigated. The simulation results show that if the data has low tail dependence, the proposed distribution performs better compared to the most entropic copula distribution based on Spearman's coefficient. Finally, using the monthly rainfall series data of Zahedan station, the application of this method in the analysis of hydrological data is investigated.

The concept of entropy has been widely extended to other fields, including information theory and economic research. The economic financial sector of any country is the supplier of financial resources and real economic activities, which are divided into two parts: the money market and the capital market. In this paper, two criteria, approximate entropy and standard deviation have been used to measure the fluctuations of the four indicators of the Tehran Stock Exchange to check that another criterion other than the standard deviation can be used to measure the fluctuations of the stock exchange indices. The data are for the years 88 to 95. The results show that the maximum amount of data for these indicators was obtained between the years 92 to 93. After studying the reason for the fluctuation of the indicators in these years, we realized the reason for the unrealistic growth of the stock market per year. There have been 92 triples in the exchange rate in 91 and the emotional reaction of investors to the new government. The results of these two measurement criteria also indicate that in addition to the standard deviation, another method such as approximate entropy can be used to measure the fluctuations of stock indices because the results of this criterion are the same as the standard deviation.

The subject of this article is about the lifetime of solar devices consisting of number (n) of tubes. The solar energy devices, when they reach an aging stage, the tubes start to fail, the maintenance costs increase, and the production of the device decreases.The costs of solar energy device maintenance companies increase as the device gets old. Therefore, maintenance companies are looking for the age to replace the device with a new device. In this article, we searched for the best age to replace device (in aging stage) with a new device.By relying on strategy of balance the costs of tubes failure in unexpected time, we have determined the optimum time for preventive replacement of solar energy device. Then we studied the factors that influence the optimum time for preventive replacement of solar energy device.

‎A copula function is a useful tool in identifying the dependency structure of dependent data and thus fitting a proper distribution to the existing data set. In this paper, using the copula function for stock market data including three variables of financial weakness, accumulated profit, and tangible assets related to 110 Iranian trading companies from 1385 to 1389 is analyzed and especially a three-dimensional distribution of these data is appropriate. We used a variety of tools to examine the dependency type in the data set, containing the scatter, chi, and Kendall plots. We also analyze the directional and tail dependency of the data set and calculated the dependence coefficients of Kendall tau and Spearman rho. Finally, we perform a good fitness of fit test for a few well-known copula functions, so that we can get the right copula function of the data set coming from the stock market.

In this article- we study devices that derive energy from natural process (sun, wind, winter, soil, etc.) and that are replenished constantly such as fans generating electric power and solar energy devices. However, all devices are exposed to damage over time resulting in the accumulation of the damage caused by climatic fluctuations (Every geographical area is characterized by bad weather characteristics that leave damage to the device; like wind, rain and humidity) that lead to the failure of the device. These devices receive energy directly from nature in order to supply it to other systems (mechanical, electrical, etc.). A failure of the device reduces electrical-mechanical production. The companies manufacture renewable energy devices and export them to other countries in various geographical locations. The devices are used to provide electrical current in these countries. These companies seek to develop long-term protection plans against the device failure. A failed device becomes ineligible even for recycling in these companies. Therefore, the cost of the device failure and forced replacement becomes too expensive for these companies. Because of this, companies tend to find the optimal time to replace the device shortly before failure to reduce the cost of failure. In this experiment we study a device that is subject to shocks and calculate the optimal time for preventive replacement of a said device. As an example a solar energy device exposed to shocks resulting from climate fluctuations. We place this device in three different geographical locations (desert, tropical, and temperate), and calculate the optimal time for preventive replacement of the device. Finally, the results from these three locations are compared.

Different approaches to goodness of fit (GOF) testing are proposed. This survey intends to present the developments on Goodness of Fit based on entropy during the last 50 years, from the very first origins until the most recent advances for different data and models. Goodness of fit tests based on Shannon entropy was started by Vasicek in 1976 and were continued by many authors. In this paper, we describe different GOF tests constructed by authors from the beginning to now. First, the problem of GOF and different types of GOF are stated. Then, the method of GOF tests based on entropy for complete and censored data is explained and all works proposed by authors in this subject are mentioned.

Wealth distribution is one of the most important and effective factors in the economic and social stability of each society. Thus, assessing the behavior of income distribution have great importance and to do this, several indices have been introduced that their performance has been investigated in terms of precision. The main goal of this paper is to introduce the Total Time on Test (TTT) transformation and its corresponding graph as a beneficial index for measuring income inequality. We further compare its performance with the Lorentz and Zanga indices. The micro-data of Iranian household income in the period 2012-2018 has been used to analyze the performance of the proposed index. The results show that while the new index performs better than the Lorenz one, it performs as same as the Zenga index. We also introduced a new distorted model using distortion functions in the final section, and by considering the basement income distribution, the generalized version of these distributions are presented and some of their features, particularly the maximum likelihood estimator are investigated. In addition, the goodness of fit of the new distributions to the income data of citizens in Texas (Arnold 1983) and the income data of Iranian households in 2017 are other results of this article.

In this article, the total time on test  (TTT) transformation and its major properties are investigated. Then, the relationship between the TTT transformation and some subjects in reliability theory is expressed. The TTT diagram is also drawn for some well-known lifetime distributions, and a real-data analysis is performed based on this diagram. A new distorted family of distributions is introduced using the distortion function. The statistical interpretation of the new life distribution from the perspective of reliability is provided, and its survival function is derived. Finally, a generalization of the Weibull distribution is introduced using a new distortion function. A real data analysis shows its superiority in fitting in comparison to the traditional Weibull model.

   One of ‎the ‎intersecting aspects of the reliability theory and economics is investigating non-negative data generally skewed‎ ‎(lifetimes and income)‎, ‎extrapolation of a suitable model for the data and finding their characteristics‎.
The concepts of inequality measures play an important role in economic, social sciences and the other areas. In recent years, various inequality curves have been developed or investigated as the descriptors of income inequality. The Lorenz curve is a strong tool extensively used in economics to consider the inequality of income distributions and wealth. It is the graphical display of wealth distribution created by the American economist, Max Lorenz, in 1905. It plots the percentage of the total income obtained by various portions of the population when the population is ordered by the size of its income. Several alternative inequality curves have been proposed in the literature. The alternative inequality curves are considered as competitors of the classical Lorenz curve as descriptors of income inequality. The Bonferroni curve and the Zenga-2007 curve appear to be essentially the function of the Lorenz curve.
Reliability is a broad concept. It is applied whenever we expect something to behave in a certain way. It is one of the metrics that are used to measure quality. The notion of reliability, in the statistical sense, is the probability that an equipment or unit will perform the required function under the conditions specified for its operations for a given period of time. The primary concern in reliability theory is to understand the patterns in which failures occur, for different mechanisms and under varying operating environments, as a function of its age. This is accomplished by identifying the probability distribution of the lifetime represented by a non-negative random variable. Accordingly, several concepts have been developed that help in evaluating the effect of age, based on the distribution function of the lifetime random variable and the residual life X. Concepts of aging describe how a component or a system improves or deteriorates with age; and they are very serious in the reliability analysis. In reliability, several aging classes of life distributions have been presented to explain the various forms of aging.
Different order relations have been developed using measures in connection with many fields such as reliability, economics, queuing theory, survival analysis, insurance, operations research, etc.
 

     In this paper, we provide a brief review of the widely used income inequality measures, their inter relationships and their properties and we discuss on basic reliability concepts such as hazard rate, mean residual life, reversed hazard rate and reversed mean residual life in distribution function frame work.
The main aim of this paper is finding the relationship between the indices of economic inequality and reliability theory‎. For example, Zenga curve shall be interpreted as the difference in average age of components which has survived beyond age X from those which has failed before attaining age X, expressed in terms of average age of components exceeding age X. Therefore, we present some of the important results about the relationship between aging concepts and several important theorems have been proved in this subject that actually are novelty of the paper. We also present some characterizations of the reliability concept by using the Lorenz curve. ‎‎In this article‎, ‎first‎, ‎the relationship between inequality indices and reliability indices which have a very close relationship are discussed‎.‎ In fact, proofing of several propositions to express these connections is the main novelty of this article. In addition,‎ some of the ageing concepts can be expressed through inequality indices‎. ‎Finally‎, ‎to gain better understanding of the basic idea the Iranian income and expenditure data between the years 1388 to 1393 are numerically studied.

In the present work, we have examined the connection between the other existing inequality measures, the relationship of the concepts of inequality indices with certain reliability concepts are exploited to obtain characterization results for probability distributions. Further some results on a stochastic order using inequality curves are also established. Finally some numerical results were given in order to indicate the usefulness. There are many reasons to study the relationship between the reliability concepts and the inequality measures. For example, the study of the relationship between inequality indices and measurement standards of reliability makes it possible to use each of these two concepts for studying the other one‎. We are able to set some other criteria for exponentiation based on the Lorenz curve and Gini index. Also, we can obtain some new properties for the Lorenz curve, the Gini index, and the other inequality indices. Moreover, we are able to indicate that the Lorenz curve can be expended to create a variant explanation of lifetime data and vice versa and, as well, to determine the bound of the class of lifetime distributions in terms of its Lorenz curve and the other index inequalities.

The following conclusions were drawn from this research.

The bound of the class of lifetime distributions are determined in terms of its Lorenz curve and the other index inequalities.
Some interesting relationships that exist between commonly used notions in reliability theory and economic theory and reliability.
Some new properties for income inequality are obtained‎./files/site1/files/61/3.pdf

Lorenz curve is one of the most important graphical tools for describing the inequality in income, wealth and other welfare indices in a society. Therefore, the estimation of Lorenz curve has always been of interest to researchers in the social sciences and economics. ‎ Hitherto, many models have been proposed for estimating the Lorentz curve. Khosravi Tanak (1396) introduced two new classes of Lorentz curve using the maximum entropy share function and based on a constraint on generalized Gini index. He showed that one of them modeled the considered data, which relates to the three Asian countries, better than alternatives. In this paper, we investigate the fitting of these models to expenditure data of urban households in Iran in the years 1388, 1390 and 1392 SH.

In this paper, a generalized lambda distribution is proposed followed by Lorenz, Bonferonni and Zenga curves. Also, inequality indices and Hierarchical Lorenz curve are given based on this distribution. Moreover, according to securities and exchange organization of Tehran income data, we compare some parametric Lorenz figures with their Hierarchical form based on the generalized lambda distribution.

One of the income distributions is the generalized Beta distribution. In this paper the family of generalized Beta distribution is introduced and it was investigated in terms of maximum entropy. Also, using MATLAB the maximum entropy estimator of the parameters of this family was found, considering variety of conditions.

Poverty and social judgment are important topics of public and private assemblies in every society. Not only is the matter of inequality income one of the main reasons of poverty but also it is considered as one of the factors of retarders of economic development. Therefore debating and judging about how income is distributed besides spreading of models of economic development is important.
One of the most typical means of measuring inequality of income distribution is Lorene curve. The main aim of this article is conducting static studies on indicators of income distribution (by emphasizing on average and Gini coefficient) in South Khorasan.
Yet with a compressive vision, we considered the average process and Gini coefficient of income and expense of south Khorasan state in 10 recent years and its station between 31 states of the country.
Therefore, the process of changes of income in south Khorasan state and the country were compared. The result shows that south Khorasan state in these years were in low condition according to the average of income and expense that in most of the years (1387and1389) had the last level that somehow shows some limitations from educational and occupational facilities in this state. The subsequent studies show the income average of Birjand city (center of the state) is almost in the same level of the country average and it shows that this limitation is in other towns rather than the center of the state.

In this paper، first the Bhattacharray and Kshirsagar bounds are introduced and then the multiparameter Bhattacharyya bound is presented in simpler and understandable form. Furthermore، the multiparameter Kshirsagar lower bound، which has not been studied yet، is obtained. Finally، by presenting some example of Log-normal distribution، the bounds are computed and compared.

The most important indicator for measuring income inequality is the Gini index. The Gini index summarizes an entire income distribution and overall degree of income inequality but have little to say about information the distribution of income between the different classes of income and the Lorenz curve. For example, when asymmetric cases that the Gini indexes for two different Lorenz curves are identical using the Gini index of income inequality alone, it is not clear that the increases in income inequality have been due to the rich getting richer or the poor become poorer. Therefore, this indicator may not be characterized as all changes in income concentration. To solve this problem, there are methods and indicators. At first, in this paper has been discussed approaches of several researchers to solve this problem by the application of skewness of Lorentz curve and then proposed a skewness coefficient as the best representation of the changes in the extremes. As an application example, the income distribution of provinces in particular for two provinces Khuzestan and Hormozgan in 2008, stressing that the two provinces are the same Gini coefficient has been examined.