|
|
|
 |
Search published articles |
 |
|
Showing 13 results for Exponential Distribution
Gholam Hossein Shahkar, Rahim Badamchizadeh,
Volume 1, Issue 1 (9-2007)
Abstract
In this paper we consider a single server queue with two phase arrival and two phase services. Arrival are Poison variables with different rates. For each input, the server provides private service with exponential distribution. The rates of services are different. The policy of service is FCFS, where the server changes the king of service according to the customer in the front of queue. After the completion of each service, the server either goes for a vacation with probability (1-theta), or may continue to server the next customer with probability theta, if any. Otherwise, it remains in the system until a customer arrives. Vacation times are assumed to have exponential distribution. We obtain steady-state probability generating function for queue size distribution for each input and expected busy period.
Mohamad Babazadeh, Sadegh Rezaee, Mousa Abdi,
Volume 6, Issue 1 (8-2012)
Abstract
In this paper, a new three-parameter lifetime distribution is introduced by combining an extended exponential distribution with a logarithmic distribution. This flexible distribution has increasing, decreasing and upside-down bathtub failure rate shapes. Various properties of the proposed distribution are discussed. The estimation of the parameters attained by EM algorithm and their asymptotic variance and covariance are obtained. In order to assess the accuracy of the approximation of variance and covariance of the maximum likelihood estimator, a simulation study is presented to illustrate the properties of distribution.
Ghobad Barmalzan, Abedin Haidari, Maryam Abdollahzade,
Volume 6, Issue 2 (2-2013)
Abstract
Suppose there are two groups of independent exponential random variables, where the first group has different hazard rates and the second group has common hazard rate. In this paper, the various stochastic orderings between their sample spacings have studied and introduced some necessary and sufficient conditions to equivalence of these stochastic ordering. Also, for the special case of sample size two, it is shown that the hazard rate function of the second sample spacing is Shcur-concave in the inverse vector of parameters.
Samaneh Jalambadanis, Mostafa Razmkhah,
Volume 6, Issue 2 (2-2013)
Abstract
In a sequence of multivariate random variables, when the experimenter is interested in ordering one of the variables, the corresponding ordered random variables are referred to as concomitants. In this paper, the distribution properties of the bivariate concomitants of record values and order statistics are first studied. Then, by considering the trivariate pseudo exponential family, the amount of Fisher information contained in these random variables is investigated.
Ghobad Barmalzan, Abedin Heidari,
Volume 7, Issue 1 (9-2013)
Abstract
Suppose there are two groups of random variables, one with independent and non-identical distributed and another with independent and identical distributed. In this paper, for the case when the size of groups are not equal, and all of the underlying random variables have exponential distribution, the necessary and sufficient conditions are obtained for establishing the mean residual life, hazard rate and dispersive orders between the second order statistics of two groups. Moreover, when random variables follow the Weibull distribution, the hazard rate, dispersive and likelihood ratio order between the second order statistics from two groups are investigated.
Eisa Mahmoudi, Reyhaneh Lalehzari, Ghahraman Roughani,
Volume 11, Issue 1 (9-2017)
Abstract
We consider the purely sequential procedure for estimating the scale parameter of an exponential distribution, when the risk function is bounded by the known preassigned number. In this paper, we provide explicit formulas for the expectation of the total sample size. Also, we propose how to adjust the stopping variable so that the risk is uniformly bounded by a known preassigned number. In the end, the performances of the proposed methodology are investigated with the help of simulations.
Azadeh Kiapour,
Volume 11, Issue 1 (9-2017)
Abstract
Usually, we estimate the unknown parameter by observing a random sample and using the usual methods of estimation such as maximum likelihood method. In some situations, we have information about the real parameter in the form of a guess. In these cases, one may shrink the maximum likelihood or other estimators towards a guess value and construct a shrinkage estimator. In this paper, we study the behavior of a Bayes shrinkage estimator for the scale parameter of exponential distribution based on censored samples under an asymmetric and scale invariant loss function. To do this, we propose a Bayes shrinkage estimator and compute the relative efficiency between this estimator and the best linear estimator within a subclass with respect to sample size, hyperparameters of the prior distribution and the vicinity of the guess and real parameter. Also, the obtained results are extended to Weibull and Rayleigh lifetime distributions.
Mehran Naghizadeh Qomi, Maryam Vahidian,
Volume 11, Issue 2 (3-2018)
Abstract
The problem of finding tolerance intervals receives very much attention in researches and is widely applied in industry. Tolerance interval is a random interval that covers a proportion of the considered population with a specified confidence level. In this paper, the statistical tolerance limits are expressed for lifetime of k out of n systems with exponentially distributed component lifetimes. Then, we compute the accuracy of proposed tolerance limits and the number of failures needed to attain a desired accuracy level based on type-II right censored data. Finally, we extend our results to the Weibull distribution.
Marjan Zare, Akbar Asgharzadeh, Seyed Fazel Bagheri,
Volume 14, Issue 1 (8-2020)
Abstract
In this paper, the smallest confidence region is obtained for the location and scale parameters of the two-parameter exponential distribution. For this purpose, we use constrained optimization problems. We first provide some suitable pivotal quantities to obtain a balanced confidence region. We then obtain the smallest confidence region by minimizing the area of the confidence region using the Lagrangian method. Two numerical examples are presented to illustrate the proposed methods. Finally, some applications of proposed joint confidence regions in hypothesis testing and the construction of confidence bands are discussed.
Mousa Abdi, Mohsen Madadi, Ahad Jamalizadeh,
Volume 14, Issue 2 (2-2021)
Abstract
In this article, a mixture of multivariate normal and standard exponential distributions is investigated. It is shown that the range of skewness and kurtosis coefficients for this distribution is wider than that of the skew-normal distribution. Some properties of this distribution, such as characteristic function, moment generating function, four first moments, skewness and kurtosis of distribution are presented. Also, the distribution of offine transformations and canonical forms of distribution are derived. The maximum likelihood estimation of parameters of the model is computed by using an EM algorithm. To investigate the suitability and efficiency of the model, a simulation study is presented. Finally, two numerical examples with real data sets are studied.
Abedin Haidari, Mostafa Sattari, Ghobad Barmalzan,
Volume 16, Issue 1 (9-2022)
Abstract
Consider two parallel systems with their component lifetimes following a generalized exponential distribution. In this paper, we introduce a region based on existing shape and scale parameters included in the distribution of one of the systems. If another parallel system's vector of scale parameters lies in that region, then the likelihood ratio ordering between the two systems holds. An extension of this result to the case when the lifetimes of components follow exponentiated Weibull distribution is also presented.
Doctor Masoumeh Akbari, Mrs Arefeh Kasiri, Doctor Kambiz Ahmadi,
Volume 17, Issue 1 (9-2023)
Abstract
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.
Mehran Naghizadeh Qomi, Zohre Mahdizadeh,
Volume 19, Issue 1 (9-2025)
Abstract
This paper investigates repetitive acceptance sampling inspection plans of lots based on type I censoring when the lifetime has a Tsallis q-exponential distribution. A repetitive acceptance sampling inspection plan is introduced, and its components, along with the optimal average sample number and the operating characteristic value of the plan, are calculated under the specified values for the parameter of distribution and consumer's and producer's risks using a nonlinear programming optimization problem. Comparing the results of the proposed repetitive acceptance sampling plan with the optimal single sampling inspection plan demonstrates the efficiency of the repetitive acceptance sampling plan over the single sampling plan. Moreover, repetitive sampling plans with a limited linear combination of risks are introduced and compared with the existing plan. Results of the introduced plan in tables and figures show that this plan has a lower ASN and, therefore, more efficiency than the existing design. A practical example in the textile industry is used to apply the proposed schemes.
|
|
