توزیع f

Drought is one of the most important concepts in hydrology, which has gained increased significance in recent years, and the results of its modeling and analysis are crucial for risk assessment and management. This study examines drought at the Zahedan station during the statistical period from 1951 to 2017 using the standardized precipitation index and explains multivariate data modeling methods using Vine Copulas. Various models are compared using goodness-of-fit criteria, and the best model is selected. Additionally, joint return periods are calculated and analyzed.

‎The cost function and the system ‎s‎tationary‏‎ probability are two key criteria in the design of queuing systems. In this paper, the aim is to design a single server queuing models with infinite capacity, where the service times in the first model and the interarrival times in the second model are assumed to have an Erlang distribution. For this purpose, a new index based on the cost function and the system reliability probability is introduced, the larger of which indicates the optimality of the model. Several numerical examples and an applied example are presented to explain the computational details of the proposed method.

Marshall-Olkin introduced a family of distributions which obtained by adding a parameter into other distributions. Santoz-Neto etal study an extended Weibull distribution. In this paper two Raiyle and Pareto extended weibull are studied under some momemts and Bayesian methods with some loss functions such as squared error, entropy, linex, squared error in logarithm and modified linex. Also the MCMC method are study for these two distributions.

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The mixed effects model is one of the powerful statistical approaches used to model the relationship between the response variable and some predictors in analyzing data with a hierarchical structure. The estimation of parameters in these models is often done following either the least squares error or maximum likelihood approaches. The estimated parameters obtained either through the least squares error or the maximum likelihood approaches are inefficient, while the error distributions are non-normal.   In such cases, the mixed effects quantile regression can be used. Moreover, when the number of variables studied increases, the penalized mixed effects quantile regression is one of the best methods to gain prediction accuracy and the model's interpretability. In this paper, under the assumption of an asymmetric Laplace distribution for random effects, we proposed a double penalized model in which both the random and fixed effects are independently penalized. Then, the performance of this new method is evaluated in the simulation studies, and a discussion of the results is presented along with a comparison with some competing models. In addition, its application is demonstrated by analyzing a real example.

The exact distribution of many applicable statistics could not be accessible in various statistical inference problems. To deal with such an issue in the large sample problem, an approach is to obtain the asymptotic distribution. In this article, we have expressed the asymptotic distribution of multivariate statistics class approximated by averages based on the Taylor expansion. Then, the asymptotic distribution of an empirical Mahalanobis depth-based statistic is obtained, and the statistic is applied to test the scale difference between two multivariate distributions. Simulation studies are carried out to explore the behavior of the asymptotic distribution of the test statistic. A real data example illustrating the use of the test is also presented.

In this paper, quantile-based dynamic cumulative residual and failure extropy measures are introduced. For a presentation of their applications, first, by using the simulation technique, a suitable estimator is selected to estimate these measures from among different estimators. Then, based on the equality of two extropy measures in terms of order statistics, symmetric continuous distributions are characterized. In this regard, a measure of deviation from symmetry is introduced and how it is applied is expressed in a real example. Also, among the common continuous distributions, the generalized Pareto distribution and as a result the exponential distribution are characterized, and based on the obtained results, the exponentiality criterion  of a distribution is proposed.

In this article, the optimal model is determined for the family of models ‎$‎‎‎{E_r/M/1, rin N}‎$‎ with interarrival times with Erlang distribution‎‏ ‎and service times with exponential distribution‎. The method of choosing the optimal model is that first, a cost function is introduced, and then a new index is introduced according to the cost function and the ‎stationary‎ probability of the system called ‎‏‎‎$‎‎‎SER‎$‎.‎‏ A model with a larger ‎$‎SER‎$‎ index is ‎optimal.‎ Numerical analysis is also used to describe the method of determining optimal ‎model.

In risk models, the ruin probabilities and ‎Lundberg‎ bound are calculated despite knowing the statistical distribution of random variables. In the present paper, for collective risk model and discrete time risk model of insurance company for independent and identically distributed claims with light-tailed distribution, the infinite time ruin probabilities are computed using Lundberg bound, moreover the general forms of density functions of random variables of claim sizes are derived. ‎‎‎For some special cases in the discrete time risk model, the density functions of claim sizes have the shifted geometric distribution, and for the collective risk model, they always have an exponential distribution.‎ ‎ ‎‎Presenting the numerical examples of infinite time ruin probabilities and the simulated values of these probabilities and the Lundberg bound are the final results of this article.

‎Information inequalities have many applications in estimation theory and statistical decision making‎. ‎This paper describes the application of an information inequality to make the minimax decision in the framework of Bayesian theory‎. ‎In this way‎, ‎first a fundamental inequality for Bayesian risk is introduced under the square error loss function and then its applications are expressed in determining asymptotically and locally minimax estimators in the case of univariate and multivariate‎. ‎In the case that the parameter components are orthogonal‎, ‎the asymptotic-local minimax estimators are obtained for a function of the mean vector and the covariance matrix in the multivariate normal distribution‎. ‎In the end‎, ‎the bounds of information inequality are calculated under a general loss function‎.

In this paper, the collective risk model of an insurance company with constant surplus initial and premium when the claims are distributed as Exponential distribution and process number of claims distributed as Poisson distribution is considered. It is supposed that the reinsurance is done based on excess loss, which in that insurance portfolio, the part of total premium is the share of the reinsurer. A general formula for computing the infinite time ruin probability in the excess loss reinsurance risk model is presented based on the classical ruin probability. The random variable of the total amount of reinsurer's insurer payment in the risk model of excess loss reinsurance is investigated and proposed explicit formulas for calculating the infinite time ruin probability in the risk model of excess loss reinsurance. Finally, the results are examined for Lindley and Exponential distributions with numerical data.

This paper presents the inverse Weibull-Poisson distribution to fit censored lifetime data. The parameters of scale, shape and failure rate are considered in terms of estimation and hypothesis testing, so the parameters are estimated under the type-II of censorship using the maximum likelihood and Bayesian methods. In Bayesian analysis, the parameters are estimated under different loss functions. The simulation section presents the symmetric confidence interval and HPD, and the estimators are compared using statistical criteria. Finally, the model's goodness of fit is evaluated using an actual data set.

In probability theory, a random variable (vector) is divided into discrete, absolutely continuous, singular continuous, and a mixture of them. Absolutely discrete and continuous random variables (vectors) have been extensively studied in various probability and statistics books. However, less attention has been paid to the issue of singular continuous distributions and mixture distributions, part of which is singular continuous. In this article, an example of ‎singular‎ random vectors is given. Also, examples of mixture random vectors are presented whose distribution function is a convex linear combination of discrete, absolutely ‎continuous,‎ and continuous distribution functions.

Profile monitoring is usually faced by control charts and mostly the response variable is observable in those problems‎. ‎We confront here with a similar problem where the values of the reward function are observed instead of the response variable vector and we use the dart model to make it easier to understand‎. ‎Supposing there exists at most one change-point‎, ‎a sequence of independent points resulted by darts throws is observed and the estimation of parameters and the change-point (if there exists any) are presented using the‎ ‎frequentist and Bayesian approaches‎. ‎In both the approaches‎, ‎two possible precision scalar and matrix are studied separately‎. ‎The results are examined through a simulation study and the methods applied on a real data‎.

In this paper, the lifetime model based on series systems with a random number of components from the family of power series distributions has been considered. First, some basic theoretical results have been obtained, which have been used to optimize the number of components in series systems. The average lifetime of the system, the cost function, and the total time on test have been used as an objective function in optimization. The issue has been investigated in detail when the lifetimes of system components have Weibull distribution, and the number of components has geometric, logarithmic, or zero-truncated Poisson distributions. The results have been given analytically and numerically. Finally, a real data set has been used to illustrate the obtained results.

Wind speed probabilistic distributions are one of the main wind characteristics for the evaluation of wind energy potential in a specific region.  In this paper, 3-parameter Log-Logistic distribution is introduced and it compared with six used statistical models for the modeling the actual wind speed data reported of Tabriz and Orumiyeh stations in Iran. The maximum likelihood estimators method via Nelder–Mead algorithm is utilized for estimating the model parameters. The flexibility of proposed distributions is measured according to the coefficient of determination, Chi-square test, Kolmogorov-Smirnov test, and root mean square error criterion. Results of the analysis show that 3-parameter Log-Logistic distribution provides the best fit to model the annual and seasonal wind speed data in Orumiyeh station and except summer season for Tabriz station. Also, wind power density error is estimated for the proposed different distributions.

Many populations encountered in survival analysis are often not homogeneous. Individuals are flexible in their susceptibility to causes of death, response to treatment and influence of various risk factors. Ignoring this heterogeneity can result in misleading conclusions. To deal with these problems, the proportional hazard frailty model was introduced. In this paper, the frailty model is explained as the product of the frailty random variable and baseline hazard rate. We examine the fit of the frailty model to the right censored data from in the presence of explanatory variables (observable variables) and use it as a practical example to fit the frailty model to the data by considering the Weibull basis distribution and exponential in the likelihood functions. It is used to estimate the model parameters and compare the fit of the models with different criteria.

In this paper a new four-parameter lifetime distribution named “the exponentiated Lomax – Rayleigh (E-LR) distribution” has been suggested that it has an increasing hazard rate for modeling lifetime data. The Lomax distribution has applications in economics, actuarial modelling, reliability modeling, lifetime and queuing problems and biological sciences. In this paper Firstly, the mathematical and statistical characteristics of the proposed distribution are presented, then the applications of the new distribution are studied using the real data set. Its first moment about origin and moments about mean have been obtained and expressions for skewness, kurtosis has been given. Various mathematical and statistical properties of the proposed distribution have been discussed. Estimation of its parameter has been discussed using the method of maximum likelihood. In the end, two applications of the new distribution have been discussed with two real lifetime data sets. The results also confirmed the suitability of the presented models for real data collection.

The Bayesian estimation of the stress-strength parameter in Lomax distribution under the progressive hybrid censored sample is considered in three cases. First, assuming the stress and strength are two random variables with a common scale and different shape parameters. The Bayesian estimations of these parameters are approximated by Lindley method and the Gibbs algorithm. Second, assuming the scale parameter is known, the exact Bayes estimation of the stress-strength parameter is obtained. Third, assuming all parameters are unknown, the Bayesian estimation of the stress-strength parameter is derived via the Gibbs algorithm. Also, the maximum likelihood estimations are calculated, and the usefulness of the Bayesian estimations is confirmed, in comparison with them. Finally, the different methods are evaluated utilizing the Monte Carlo simulation and one real data set is analyzed.

In classical statistics, the parameter of interest is estimated based on sample information and using natural estimators such as maximum likelihood estimators. In Bayesian statistics, the Bayesian estimators are constructed based on prior knowledge and combining with it sample information. But, in some situations, the researcher has information about the unknown parameter as a guess. Bayesian shrinkage estimators can be constructed by Combining this non-sample information with sample information together with the prior knowledge, which is in the area of semi-classical statistics. In this paper, we introduce a class of Bayesian shrinkage estimators for the Weibull scale parameter as a generalization of the estimator at hand and consider the bias and risk of them under LINEX loss function. Then, the proposed estimators are compared using a real data set.

In this paper, we investigate the confidence interval for the parameter of the common correlation coefficient of several bivariate normal populations. To do this, we use the confidence distribution approach. By simulation studies and using the concepts of coverage probability and expected length, We compare this method with the generalized variable approach. Results of simulation studies show that the coverage probability of the proposed method is close to the nominal level in all situations and also, in most cases, the expected length of this method is less than that of the generalized variable approach. Finally, we present two real examples to apply this approach.