ابوذر بازیاری

The ability of insurers to pay claims is one of the most important issues in the management of insurance companies. In this paper, the collective risk model of insurance company with constant premium and compound Poisson process over a period of time is considered. For a general class of claim sizes with light tailed and heavy tailed distributions, a formula for computing the finite time ruin probability is obtained using the probability transformation, then the matrix form of the presented formula by the transformation matrix and continuous time Markov chain generating matrix is rewritten. Also, using simulation paths from the risk process for claim sizes with Exponential, Normal and Pareto distributions with different values of initial reserve at the different times, in addition to compute the finite time ruin probabilities and unbiased confidence intervals, their values estimated for transformation matrix and Markov chain generating matrix.

In the excess loss reinsurance risk model, the amount of insurance premium paid by the company is influential in the ruin of that company. In this paper, the premium function is presented based on the expected amount of total payments of the reinsurer to the assigning insurer, the constraint on this function is investigated, and for the claims with any arbitrary distribution, the contour plots are drawn and with presenting optimization algorithm, infinite time ruin probability function will be minimum for different values of initial capital and threshold value. Finally, the excess loss reinsurance risk model with non-exponential claims is considered, and the infinite time ruin probability is calculated with numerical examples.

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.

In this paper, the individual risk model of the insurance company with dependent claims is considered and assumes that the binary vector of random variables of claim sizes is independent. Also, they have a common joint distribution function. A recursive formula for infinite time ruin probability is obtained according to the initial reserve and joint probability density function of random variables of claim sizes using probability inequalities and the induction method. Some numerical examples and simulation studies are presented for checking the results related to the light-tailed bivariate Poisson, heavy-tailed Log-Normal and Pareto distributions. The results are compared for Farlie–Gambel–Morgenstern and bivariate Frank copula functions. The effect of claims with heavy-tailed distributions on the ruin probability is also investigated.

Wavelet analysis is one of the useful techniques in mathematics which is used much in statistics science recently. In this paper, in addition to introduce the wavelet transformation, the wavelet threshold estimation of semiparametric regression model with correlated errors with having Gaussian distribution is determined and the convergence ratio of estimator computed. To evaluate the wavelet threshold estimation, the block function and sinusoidal function are used as objective functions and using the simulation method the average of mean square error and standard deviation of this estimator are compared with the average of mean square error and standard deviation of kernel method. Also, the wavelet semiparametric regression model has been fitted to data on the growth rate of the teeth.

In this paper, a generalization of the Gumbel distribution as the cubic transmuted Gumbel distribution based on ‎the ‎cubic ranking transmutation map is introduced. It is shown that for some of the parameters, the proposed density function is mesokurtic and for others parameters the density function is platykurtic function. The statistical properties of new distribution, consist of survival function, hazard function, moments and moment generating function have been studied. The parameters of cubic transmuted Gumbel distribution are estimated using the maximum likelihood method. Also, the application of the cubic transmuted Gumbel distribution is shown with two numerical examples and compared with Gumbel distribution and transmuted Gumbel distribution. Finally, it is shown that for a data set, the proposed cubic transmuted Gumbel distribution is better than Gumbel distribution and transmuted Gumbel distribution.

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.

In this paper, first, the generalized lambda distribution and the characteristics of this distribution are introduced. The concept of resistance stress is fully explained and the reliability of a system from the perspective of resistance stress is examined. Also, the mathematical form of the resistance stress parameter in the generalized lambda distribution has been calculated. The estimation of the parameters has been investigated by the moments method‎‎ and ‎for different parameters values the graph of generalized lambda distribution is drawn ‎‎and resistance stress parameter calculated. With a real example the application of the results is illustrated.‎‎

In this paper, the wavelet estimators of the nonparametric regression function based on the various thresholds under the mixture prior distribution and the mean square error loss function in Bosove space are computed. Also, using a simulation study the optimality of different wavelet thresholding estimators such as posterior mean, posterior median, Bayes factor, universal threshold and sure threshold are investigated. The results show that the average mean square error of sure threshold estimator is less than the other obtained estimators.

Unfortunately, in the recent few years, decreasing the level of educational motivation among students at various levels of education has been increasing and has plagued many of the university educational units in the country and this can have devastating and irreparable effects in the near future. In this research, using statistical analysis of the number of questionnaires, social factors are investigated on the motivation of Bushehr Persian Gulf University students and relationship between each of variables such as job status, the income of educated, gender, marital status, family income, presented content in the textbooks, university educational facilities, and weather conditions have been studied with students' educational motivation. The unequal two-stage cluster sampling method is used to collect the sample data and the required information and multivariate factor analysis used to examine the internal correlations of variables and to find the main factors by predicting the variance of variables by the factors. Also, the effect of variables on the students' educational motivation has been studied.

In this article, we wish to find and select appropriate estimators for statistical population density function using line transect sampling in the present of detection functions with light and heavy tailed distributions. Also it is shown that how the type of detection function could be effective in selection of the best estimator and then we propose a unbiased estimators that has the lower variance than the existed estimators. the simulation results show that if detection functions have heavy tailed distribution, then the new estimators have least mean square error.