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- Generating function (2)
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Articles 1 - 12 of 12
Full-Text Articles in Statistics and Probability
Proportional Reversed Hazard Rate Models With Exponential Baseline, G. Barmalzan, H. Saboori
Proportional Reversed Hazard Rate Models With Exponential Baseline, G. Barmalzan, H. Saboori
Applications and Applied Mathematics: An International Journal (AAM)
The proportional hazard regression models have been used extensively in survival analysis to understand and exploit the relationship between survival time and covariates. For left censored survival times, reversed hazard rate functions are more appropriate. In this paper, we discuss a parametric proportional reversed hazard rates model using exponential baseline. The estimation for the parameters are discussed. We also assess the performance of the proposed procedure based on a large number of Monte Carlo simulations. Finally, we illustrate the proposed method using a real case example and then we show that it provides a good and better fit than the …
Stationary Analysis Of A Multiserver Queue With Multiple Working Vacation And Impatient Customers, P. Manoharan, Shakir Majid
Stationary Analysis Of A Multiserver Queue With Multiple Working Vacation And Impatient Customers, P. Manoharan, Shakir Majid
Applications and Applied Mathematics: An International Journal (AAM)
We consider an M/M/c queue with multiple working vacation and impatient customers. The server serves the customers at a lower rate rather than completely halts the service during this working vacation period. The impatience of the customer’s arises when they arrive during the working vacation period, where the service rate of the customer’s is lower than the normal busy period. The queue is analyzed for multiple working vacation policies. The policy of a MWV demands the server to keep taking vacation until it finds at least a single customer waiting in the system at an instant vacation completion. On returning …
Transient Solution Of M[X1],M[X2]/G1,G2/1 With Priority Services, Modified Bernoulli Vacation, Bernoulli Feedback, Breakdown, Delaying Repair And Reneging, G. Ayyappan, J. Udayageetha
Transient Solution Of M[X1],M[X2]/G1,G2/1 With Priority Services, Modified Bernoulli Vacation, Bernoulli Feedback, Breakdown, Delaying Repair And Reneging, G. Ayyappan, J. Udayageetha
Applications and Applied Mathematics: An International Journal (AAM)
This paper considers a queuing system which facilitates a single server that serves two classes of units: high priority and low priority units. These two classes of units arrive at the system in two independent compound Poisson processes. It aims to decipher average queue size and average waiting time of the units. Under the pre-emptive priority rule, the server provides a general service to these arriving units. It is further assumed the server may take a vacation after serving the last high priority unit present in the system or at the service completion of each low priority unit present in …
Analysis Of A M/M/C Queue With Single And Multiple Synchronous Working Vacations, Shakir Majid, P. Manoharan
Analysis Of A M/M/C Queue With Single And Multiple Synchronous Working Vacations, Shakir Majid, P. Manoharan
Applications and Applied Mathematics: An International Journal (AAM)
We consider a M/M/c queuing system with synchronous working vacation and two different policies of working vacation i.e. a multiple working vacation policy and a single working policy. During a working vacation the server does not completely halts the service rather than it will render service at a lower rate. In synchronous vacation policy all the servers leave for a vacation simultaneously, when the server finds the system empty after finishing serving a customer. In multiple working vacation (MWV) policy the servers continue to take vacation till they find the system nonempty at a vacation completion instant. Single working vacation …
Exponentiated Weibull-Exponential Distribution With Applications, M. Elgarhy, M. Shakil, B. M. Golam Kibria
Exponentiated Weibull-Exponential Distribution With Applications, M. Elgarhy, M. Shakil, B. M. Golam Kibria
Applications and Applied Mathematics: An International Journal (AAM)
In this article, a new four-parameter continuous model, called the exponentiated Weibull exponential distribution, is introduced based on exponentiated Weibull-G family (Hassan and Elgarhy, 2016). The new model contains some new distributions as well as some former distributions. Various mathematical properties of this distribution are studied. General explicit expressions for the quantile function, expansion of distribution and density functions, moments, generating function, Rényi and q – entropies, and order statistics are obtained. The estimation of the model parameters is discussed using maximum likelihood method. The practical importance of the new distribution is demonstrated through real data set where we compare …
Farlie-Gumbel-Morgenstern Family: Equivalence Of Uncorrelation And Independence, G. Barmalzan, F. Vali
Farlie-Gumbel-Morgenstern Family: Equivalence Of Uncorrelation And Independence, G. Barmalzan, F. Vali
Applications and Applied Mathematics: An International Journal (AAM)
Considering the characteristics of the bivariate normal distribution, in which uncorrelation of two random variables is equivalent to their independence, it is interesting to verify this problem in other distributions. In other words, whether the multivariate normal distribution is the only distribution in which uncorrelation is equivalent to independence. In this paper, we answer to this question and establish generalized Farlie-Gumbel-Morgenstern (FGM) family is another family of distributions under which uncorrelation is equivalent to independence.
On Some Statistics For Testing The Skewness In A Population: An Empirical Study, Yawen Guo, B. M. Golam Kibria
On Some Statistics For Testing The Skewness In A Population: An Empirical Study, Yawen Guo, B. M. Golam Kibria
Applications and Applied Mathematics: An International Journal (AAM)
The purpose of this paper is to propose some test statistics for testing the skewness parameter of a distribution, not limited to a normal distribution. Since a theoretical comparison is not possible, a simulation study has been conducted to compare the performance of the test statistics. We have compared both parametric methods (classical method with normality assumption) and non-parametric methods (bootstrap in Bias Corrected Standard Method, Efron’s Percentile Method, Hall’s Percentile Method and Bias Corrected Percentile Method). Our simulation results indicate that the power of the tests differ significantly across sample sizes, the choice of alternative hypotheses and methods one …
Fitting Skew Distributions To Iranian Auto Insurance Claim Data, Ramin Kazemi, Abdollah Jalilian, Akram Kohansal
Fitting Skew Distributions To Iranian Auto Insurance Claim Data, Ramin Kazemi, Abdollah Jalilian, Akram Kohansal
Applications and Applied Mathematics: An International Journal (AAM)
In actuary, the derivation of loss distributions from insurance data is of great interest. Fitting an adequate distribution to real insurance data is not an easy task, mainly due to the nature of the data, which shows several features to be accounted for. Although, because of its stochastic and numerical simplicity, it is often assumed that the involved financial risk factors are normally distributed, but empirical studies indicate that most of financial risk factors have distributions with high peaks and heavy tails. Thus, it is important in the actuarial science to model insurance risks with skewed distributions. Claims size data …
Evaluation Of Some Reliability Characteristics Of A Single Unit System Requiring Two Types Of Supporting Device For Operations, Ibrahim Yusuf, Nura J. Fagge
Evaluation Of Some Reliability Characteristics Of A Single Unit System Requiring Two Types Of Supporting Device For Operations, Ibrahim Yusuf, Nura J. Fagge
Applications and Applied Mathematics: An International Journal (AAM)
This study presents the reliability assessment of a single unit connected to two types of external supporting devices for its operation. Each type of external supporting device has two copies I and II on standby. First order differential difference equations method is used to obtain the explicit expression for the steady state availability, busy period due to failure of type I and II supporting devices of repairmen, steady-state availability and profit function. Based on assumed numerical values given to system parameters, graphical illustrations are given to highlight important results. Comparisons are performed to highlight the impact of unit failure and …
An M/G/1 Retrial Queue With Single Working Vacation, S. P. Bala Murugan, K. Santhi
An M/G/1 Retrial Queue With Single Working Vacation, S. P. Bala Murugan, K. Santhi
Applications and Applied Mathematics: An International Journal (AAM)
We consider an M=G=1 retrial queue with general retrial times and single working vacation. During the working vacation period, customers can be served at a lower rate. Both service times in a vacation period and in a service period are generally distributed random variables. Using supplementary variable method we obtain the probability generating function for the number of customers and the average number of customers in the orbit. Furthermore, we carry out the waiting time distribution and some special cases of interest are discussed. Finally, some numerical results are presented.
Exponential Chain Dual To Ratio Cum Dual To Product Estimator For Finite Population Mean In Double Sampling Scheme, Yater Tato, B. K. Singh
Exponential Chain Dual To Ratio Cum Dual To Product Estimator For Finite Population Mean In Double Sampling Scheme, Yater Tato, B. K. Singh
Applications and Applied Mathematics: An International Journal (AAM)
This paper considers an exponential chain dual to ratio cum dual to product estimator for estimating finite population mean using two auxiliary variables in double sampling scheme when the information on another additional auxiliary variable is available along with the main auxiliary variable. The expressions for bias and mean square error of the asymptotically optimum estimator are identified in two different cases. The optimum value of the first phase and second phase sample size has been obtained for the fixed cost of survey. To illustrate the results, theoretical and empirical studies have also been carried out to judge the merits …
A Semiparametric Estimation For The Nonlinear Vector Autoregressive Time Series Model, Rahman Farnoosh, Mahtab Hajebi, Seyed J. Mortazavi
A Semiparametric Estimation For The Nonlinear Vector Autoregressive Time Series Model, Rahman Farnoosh, Mahtab Hajebi, Seyed J. Mortazavi
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, the nonlinear vector autoregressive model is considered and a semiparametric method is proposed to estimate the nonlinear vector regression function. We use Taylor series expansion up to the second order which has a parametric framework as a representation of the nonlinear vector regression function. After the parameters are estimated through the least squares method, the obtained nonlinear vector regression function is adjusted by a nonparametric diagonal matrix, and the proposed diagonal matrix is also estimated through the nonparametric smooth-kernel approach. Estimating the parameters can yield the desired estimate of the vector regression function based on the data. …