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Showing 6 results for Pareto Distribution
Anita Abdollahi,
Volume 20, Issue 2 (10-2015)
Abstract
In this paper, after stating the characteristicof some of continuous distributions including, gamma, Crovelli’s
gamma, Rayleigh, Weibull, Pareto, exponential and generalized gamma distribution with each other,these distributions
were fit on drought data of Guilan state and the best distribution was presented. Then, severity and duration of
the drought of different sites were investigated using standardized precipitation index.
Masoud Ghasemi Behjani, Milad Asadzadeh,
Volume 22, Issue 1 (12-2017)
Abstract
In this paper we propose a utility function and obtain the Bayese stimate and the optimum sample size under this utility function. This utility function is designed especially to obtain the Bayes estimate when the posterior follows a gamma distribution. We consider a Normal with known mean, a Pareto, an Exponential and a Poisson distribution for an optimum sample size under the proposed utility function, so that minimizes the cost of sampling. In this process, we use Lindley cost function in order to minimize the cost. Here, because of the complicated form of computation, we are unable to solve it analytically and use the mumerical methids to get the optimum sample size.
Ali Hedayati, Esmaile Khorram, Saeid Rezakhah,
Volume 22, Issue 2 (3-2018)
Abstract
Maximum likelihood estimation of multivariate distributions needs solving a optimization problem with large dimentions (to the number of unknown parameters) but two- stage estimation divides this problem to several simple optimizations. It saves significant amount of computational time. Two methods are investigated for estimation consistency check. We revisit Sankaran and Nair's bivariate Pareto distribution as an example. Two data sets (simulated data and real data) have been analyzed for illustrative purposes.
Anita Abdollahi Nanvapisheh, ,
Volume 23, Issue 2 (3-2019)
Abstract
In this paper, a new distribution is introduced, which is a generalization of a well-known distribution. This distribution is flexible and applies to income data modeling. We first provide some of the mathematical and distributional properties of this new model and then, to demonstrate the flexibility the new distribution, we will present the applications of this distribution with real data. Data fitting results confirm the appropriateness of this new model for the real data set.
,
Volume 24, Issue 2 (3-2020)
Abstract
One of the most common censoring methods is the progressive type-II censoring. In this method of censoring, a total of $n$ units are placed on the test, and at the time of failure of each unit, some of the remaining units are randomly removed. This will continue to record $m$ failure times, where $m$ is a pre-determined value, and then the experiment ends. The problem of determining the optimal censoring scheme in the progressive type-II censoring has been studied so far by considering different criteria. Another issue in the progressive type-II censoring is choosing the sample size at the start of the experiment, namely $n$. In this paper, assuming the Pareto distribution for the data, we will determine the optimal sample size, $n_ {opt}$, as well as the optimal censoring scheme by means of the Fisher Information. Finally, to evaluate the results, numerical calculations have been presented by using $R$ software.
Dr. Abouzar Bazyari,
Volume 28, Issue 2 (3-2024)
Abstract
Insurance companies are modeled with mathematical and statistical models in terms of their random structure. In this paper, the individual risk model of insurance company with different interest rates in a period of time is considered and assumed that the interest rates have the probability transition matrix with finite and countable state. The finite and infinite time ruin probabilities are computed using the conditional probability on the first claim of density function. Moreover, the upper bounds for the infinite time ruin probability are obtained using the mathematical induction. In the numerical examples, the ruin probabilities for heavy tailed distributions are compared with the obtained probabilities in Bazyari (2022) for the classical individual risk model and also, the infinite time ruin probabilities for light tailed distributions are compared with Lundberg's inequality. The results show that the existence of interest rate with probability transition matrix and having finite state leads to decrease the ruin probabilities.
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