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Showing 17 results for Probability
A Parvardeh, M Taheri, S Kamkar,
Volume 14, Issue 2 (3-2010)
Abstract
Samira Jalayeri, , ,
Volume 17, Issue 1 (9-2012)
Abstract
Implementing unequal probability sampling, without replacement, is very complex and several methods have been suggested for its performance, including : Midseno design and systematic design. One of the methods that have been introduced by Devil and Tille (1998) is the splitting design that leads to simple random sampling .in this paper by completely explaining the design, with an example, we have shown, the method to calcculate probability for each possible samples, using R software. it`s good to know that we can implement this design using the program in different communities after defining the ideal probability inclusion.
Dr. Nabaz Esmailzadeh,
Volume 18, Issue 1 (9-2013)
Abstract
The search designs first introduced in Srivastava (1975) is reviewed. In a ceritan problem, there may be some search designs with same runs. Some criteria for evaluation of search designs are the other topic in the paper. Criteria based on searching probability and expected Kullback- Leibler are reviewd. Some examples are given in each case.
Alireza Shirvani, Dr Mina Towhidi,
Volume 18, Issue 2 (3-2014)
Abstract
So far many confidence intervals were introduced for the binomial proportion. In this paper, our purpose is comparing five well known based on their exact confidence coefficient and average coverage probability.
Hossein Nadeb, Hamzeh Torabi,
Volume 21, Issue 1 (9-2016)
Abstract
Censored samples are discussed in experiments of life-testing; i.e. whenever the experimenter does not observe the failure times of all units placed on a life test. In recent years, inference based on censored sampling is considered, so that about the parameters of various distributions such as normal, exponential, gamma, Rayleigh, Weibull, log normal, inverse Gaussian, logistic, Laplace, and Pareto, has been inferred based on censored sampling.
In this paper, a procedure for exact hypothesis testing and obtaining confidence interval for mean of the exponential distribution under Type-I progressive hybrid censoring is proposed. Then, performance of the proposed confidence interval is evaluated using simulation. Finally, the proposed procedures are performed on a data set.
Mr Alireza Shirvani,
Volume 21, Issue 1 (9-2016)
Abstract
A Poisson distribution is well used as a standard model for analyzing count data. So the Poisson distribution parameter estimation is widely applied in practice. Providing accurate confidence intervals for the discrete distribution parameters is very difficult. So far, many asymptotic confidence intervals for the mean of Poisson distribution is provided. It is known that the coverage probability of the confidence interval (L(X),U(X)) is a function of distribution parameter. Since Poisson distribution is discrete, coverage probability of confidence intervals for Poisson mean has no closed form and the exact calculation of confidence coefficient, average coverage probability and maximum coverage probabilities for this intervals, is very difficult. Methodologies for computing the exact average coverage probabilities as well as the exact confidence coefficients of confidence intervals for one-parameter discrete distributions with increasing bounds are proposed by Wang (2009). In this paper, we consider a situation that the both lower and upper bounds of the confidence interval is increasing. In such situations, we explore the problem of finding an exact maximum coverage probabilities for confidence intervals of Poisson mean. Decision about confidence intervals optimality, based on simultaneous evaluation of confidence coefficient, average coverage probability and maximum coverage probabilities, will be more reliable.
, , ,
Volume 22, Issue 1 (12-2017)
Abstract
Latent class analysis (LCA) is a method of evaluating non sampling errors, especially measurement error in categorical data. Biemer (2011) introduced four latent class modeling approaches: probability model parameterization, log linear model, modified path model, and graphical model using path diagrams. These models are interchangeable. Latent class probability models express likelihood of cross-classification tables in term of conditional and marginal probabilities for each cell. In this approach model parameters are estimated using EM algorithm. To test latent class model chi-square statistic is used as a measure of goodness-of-fit. In this paper we use LCA and data from a small-scale survey to estimate misclassification error (as a measurement error) of students who had at least a failing grade as well as misclassification error of students with average grades below 14.
Ali Bahami, Ebrahim Reyhani, Ehsan Bahami,
Volume 24, Issue 1 (9-2019)
Abstract
The aim of this study, that was carried out in descriptive of the survey, is to assess the understanding and misunderstanding of the concept of probability eighth grade students. The samples of this study are, all eighth grade boy and girl students of Tehran province. The study sample,1330 eighth grade students in Tehran who were selected randomly. A random sample of 1330 students, from different public school. intelligence school, Shahed and perspicacious school randomly classified. and they were given 15 questions. which their validity has been studied by the number of math professors and teachers of mathematics and experienced math teachers. The reliability tests with Cronbach's alpha coefficien. 961 Was confirmed.After analyzing descriptive statistics, misunderstanding of the students were identified in seven groups as follow: lack of understanding rational numbers and its relationship to fractions, lack of understanding some of the concepts prerequisite, language problems, using their own methods to calculate the probability, inability to count all possible states, inappropiate generalization and the inability of the undrestanding of prerequisite problems.
Ramin Kazemi,
Volume 24, Issue 1 (9-2019)
Abstract
The goal of this paper is to introduce the contraction method for analysing the algorithms.
By means of this method several interesting classes of recursions can be analyzed as paricular cases of the general framework. The main steps of this technique is based on contraction properties of algorithm with respect to suitable probability metrics. Typlically the limiting distribution is characterized as a fixed poin of a limiting operator on the class of probability distributions.
Mojtaba Rostami, Shahram Fattahi,
Volume 25, Issue 1 (1-2021)
Abstract
Economic theories seek a scientific explanation, or prediction of economic phenomena using a set of axioms, defined expressions and theorems. Mathematically explicit economic models are one of these theories. Due to the unknown structure of each model, the existence of measurement error in economic committees, and the failure of Ceteris Paribus; the Synthetic of any economic theory requires probabilistic and statistical modeling. Therefore, understanding the current method of modeling and the importance of its proper use in economics requires economists to have an accurate knowledge of statistical modeling. The present study seeks to correct the view that although the purpose of providing statistical models is to experimentally test the claims of theories, statistical methods do not play a secondary role in economic theories, but the appropriate method of economic modeling depends on the correct use of statistical methods and probability models in the situation of making a theory.
Dr. Abouzar Bazyari,
Volume 27, Issue 1 (3-2023)
Abstract
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.
Shahrastani Shahram Yaghoobzadeh,
Volume 27, Issue 2 (3-2023)
Abstract
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.
Kamran Mirzaie, Maryam Parsaeian,
Volume 27, Issue 2 (3-2023)
Abstract
In the present article, an attempt has been made to provide a fully operational and useful guide regarding the implementation of two-stage cluster sampling plan in field research, which is one of the most widely used sampling plans according to the current conditions and facilities in the country. . In addition, for further use by researchers in this field, this article provides codes for implementing two-stage cluster sampling with unequal size based on probability proportional to size along with an example on two-stage cluster sampling with probability proportional to size (PPS) with hypothetical data using R software is included.
Hossein Samimi Haghgozar, Anahita Nazarizadeh,
Volume 28, Issue 1 (9-2023)
Abstract
Risk means a situation in which there is a possibility of deviation from a predicted result. Insurance is one of the methods of risk exposure that leads to the transfer of all or part of the risk from the insured to the insurer. Insurance policies are usually classified into two types: personal and non-life (non-life) insurance. According to this classification, any insurance policy that deals with the health of the insured person or persons is a personal insurance policy, otherwise it will be a nonlife insurance policy. Many insurances in the insurance industry are classified as non-life insurances. Fire, automobile, engineering, shipping, oil and energy insurances are examples of these insurances. Explanation and calculation of three issues in risk models are very important: the ruin probability, the time of ruin and the amount of ruin. In this article, the main and well-known results that have been obtained so far in the field of non-life insurance; Emphasizing the possibility of ruin, it is given along with various examples.
Shahrastani Shahram Yaghoobzadeh Shahrastani, Amrollah Jafari,
Volume 28, Issue 1 (9-2023)
Abstract
In this article, queunig model $M/M/1$ is Considered, in which the innterarrival of customers have an exponenial disributon with the parameter $lambda$ and the service times have an exponenial disributon with the parameter $mu$ and are independent of the interarrival times. it is also assumed that the system is active until $T$. Then, under this stopping time Bayesian, $E$-Bayesian and hierarchical Bayesian estimations of the traffic intensity parameter of this queuing model are obtained under the general entropy loss function and considering the gamma and erlang prior distributions for parameters $lambda$ and $mu$, respicctively. Then, using numerical analysis and based on a new index, Bayesian, $E$-Bayesian and hierarchical Bayesian estimations are compared.
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.
Dr. Reza Zarei, Dr. Shahram Yaghoubzadeh Shahrestani, Dr. Amrollah Jafari,
Volume 28, Issue 2 (3-2024)
Abstract
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.
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