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Articles 91 - 120 of 161

Full-Text Articles in Statistics and Probability

Approximation To Multivariate Normal Higher Dimensional Probabilities In Mixed - Data Model With Missing Responses, E. B. Samani Jun 2018

Approximation To Multivariate Normal Higher Dimensional Probabilities In Mixed - Data Model With Missing Responses, E. B. Samani

Applications and Applied Mathematics: An International Journal (AAM)

Multivariate data with mixed ordinal and continuous responses with the possibility of nonignorable missingness are often common in follow up social studies and their analysis need to be promoted. One of the standard methods of analysis is based on joint modelling. In this method, we use that simultaneously allow modelling non-ignorable mechanism and a full likelihood-based approach is used to obtain maximum likelihood estimates of parameters of joint modelling. In this approach, when the dimension of the vector responses are increased, includes somehow troubling computations which are often time-consuming. Another alternative is an approximation for multivariate normal probabilities for higher …

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Multiple-Model Multiple Imputation For Longitudinal Count Data To Address Uncertainty In Missingness Mechanism, E. J. Farahani, T. Baghfalaki Jun 2018

Multiple-Model Multiple Imputation For Longitudinal Count Data To Address Uncertainty In Missingness Mechanism, E. J. Farahani, T. Baghfalaki

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, an approach to generate imputed values for count variables to incorporate missing data mechanism uncertainty is proposed. For multiple imputation, a distribution is considered in such a manner that it can reflect missing data mechanism uncertainty. For combining the parameter estimation of these imputed data sets the rules of nested multiple imputation are used. The performance of the multiple imputations is investigated using some simulation studies. Also, a real data set is analyzed using the proposed approach.

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Estimation Of The Burr Xii-Exponential Distribution Parameters, Gholamhossein Yari, Zahra Tondpour Jun 2018

Estimation Of The Burr Xii-Exponential Distribution Parameters, Gholamhossein Yari, Zahra Tondpour

Applications and Applied Mathematics: An International Journal (AAM)

The Burr XII distribution is one of the most important distributions in Survival analysis. In this article, we introduce the new wider Burr XII-G family of distributions. A special model in the new family called Burr XII-exponential distribution that has constant, decreasing and unimodal hazard rate functions is investigated. We discuss the estimation of this distribution parameters by maximum likelihood, three modifications of maximum likelihood and Bayes methods. In Bayes method, we use the uniform, triangular and Burr XII-uniform priors for posterior analysis and obtain Bayes estimations under two different loss functions. We obtain two approximations of the Bayes estimations, …

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Profit Analysis Of A Two Unit Cold Standby System Operating Under Different Weather Conditions Subject T O Inspection, M. S. Barak, Neeraj _, Sudesh Kumari Jun 2018

Profit Analysis Of A Two Unit Cold Standby System Operating Under Different Weather Conditions Subject T O Inspection, M. S. Barak, Neeraj _, Sudesh Kumari

Applications and Applied Mathematics: An International Journal (AAM)

A system, or unit, is said to be working under normal weather conditions if the system is working under prescribed conditions as defined/stated by the definition of reliability of system/unit, otherwise the system is said to be working in abnormal weather conditions. For example, if a car with the capacity for five persons is carrying more than five persons, it will be said to be working under abnormal weather conditions. Another example, if a hydraulic machine having the capacity to lift a maximum weight of 500 tons is lifting a weight of 600 tons, then the machine is working under …

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Transmuted New Weibull-Pareto Distribution And Its Applications, Areeb Tahir, Ahmad S. Akhter, M. A. Ul Haq Jun 2018

Transmuted New Weibull-Pareto Distribution And Its Applications, Areeb Tahir, Ahmad S. Akhter, M. A. Ul Haq

Applications and Applied Mathematics: An International Journal (AAM)

this article, a generalization of the new Weibull-Pareto (NWP) distribution is derived. The quadratic equation (QRTM rank transmutation map) studied by Shaw and Buckley (2007), has been used to develop the generalization. The proposed distribution includes as special cases with the new Weibull-Pareto distribution (NWP), transmuted Weibull distribution (TW), transmuted Rayleigh (TR) distribution and transmuted exponential (TE) distribution. Various structural properties of the new distribution, including of moments, quantiles, moment generating function, mean deviations, reliability analysis, order statistics and Renyi entropy are derived. The maximum likelihood estimation method has been proposed for the estimation of the parameters of the TNWP …

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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 Dec 2017

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 …

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Stationary Analysis Of A Multiserver Queue With Multiple Working Vacation And Impatient Customers, P. Manoharan, Shakir Majid Dec 2017

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 …

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Exponentiated Weibull-Exponential Distribution With Applications, M. Elgarhy, M. Shakil, B. M. Golam Kibria Dec 2017

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 …

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Farlie-Gumbel-Morgenstern Family: Equivalence Of Uncorrelation And Independence, G. Barmalzan, F. Vali Dec 2017

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.

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Analysis Of A M/M/C Queue With Single And Multiple Synchronous Working Vacations, Shakir Majid, P. Manoharan Dec 2017

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 …

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Proportional Reversed Hazard Rate Models With Exponential Baseline, G. Barmalzan, H. Saboori Dec 2017

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 …

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On Some Statistics For Testing The Skewness In A Population: An Empirical Study, Yawen Guo, B. M. Golam Kibria Dec 2017

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 …

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Fitting Skew Distributions To Iranian Auto Insurance Claim Data, Ramin Kazemi, Abdollah Jalilian, Akram Kohansal Dec 2017

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 …

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Evaluation Of Some Reliability Characteristics Of A Single Unit System Requiring Two Types Of Supporting Device For Operations, Ibrahim Yusuf, Nura J. Fagge Dec 2017

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 …

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Exponential Chain Dual To Ratio Cum Dual To Product Estimator For Finite Population Mean In Double Sampling Scheme, Yater Tato, B. K. Singh Jun 2017

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 …

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A Semiparametric Estimation For The Nonlinear Vector Autoregressive Time Series Model, Rahman Farnoosh, Mahtab Hajebi, Seyed J. Mortazavi Jun 2017

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. …

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An M/G/1 Retrial Queue With Single Working Vacation, S. P. Bala Murugan, K. Santhi Jun 2017

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.

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Non Markovian Queue With Two Types Service Optional Re-Service And General Vacation Distribution, K. Sathiya, G. Ayyappan Dec 2016

Non Markovian Queue With Two Types Service Optional Re-Service And General Vacation Distribution, K. Sathiya, G. Ayyappan

Applications and Applied Mathematics: An International Journal (AAM)

We consider a single server batch arrival queueing system, where the server provides two types of heterogeneous service. A customer has the option of choosing either type 1 service with probability p1 or type 2 service with probability p2 with the service times follow general distribution. After the completion of either type 1 or type 2 service a customer has the option to repeat or not to repeat the type 1 or type 2 service. As soon as the customer service is completed, the server will take a vacation with probability θ or may continue staying in the system with …

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Exact Asymptotic Errors Of The Hazard Conditional Rate Kernel For Functional Random Fields, Abbes Rabhi, Sara Soltani Dec 2016

Exact Asymptotic Errors Of The Hazard Conditional Rate Kernel For Functional Random Fields, Abbes Rabhi, Sara Soltani

Applications and Applied Mathematics: An International Journal (AAM)

We consider the problem of nonparametric estimation of the kernel type estimators for the conditional cumulative distribution function and the successive derivatives of the conditional density for spatial data. More precisely, given a strictly stationary random field Z = (X, Y), we investigate a kernel estimate of the conditional hazard function of univariate response variable Y given the functional variable X. The principal aim of this paper is to give the mean squared convergence rate of the proposed estimator. Finally, we apply these theoretical results to the estimation of the conditional hazard function where we give the mean squared convergence …

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Markov Chain Profit Modelling And Evaluation Between Two Dissimilar Systems Under Two Types Of Failures, Saminu I. Bala, Ibrahim Yusuf Dec 2016

Markov Chain Profit Modelling And Evaluation Between Two Dissimilar Systems Under Two Types Of Failures, Saminu I. Bala, Ibrahim Yusuf

Applications and Applied Mathematics: An International Journal (AAM)

No abstract provided.

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Enhancement Of Heat Transfer In Elastico-Viscous Fluid Due To Nanoparticles, Where The Fluid Is Impinging Obliquely To The Stretchable Surface: A Numerical Study, Tariq Javed, Abuzar Ghaffari, Tasawar Hayat Jun 2016

Enhancement Of Heat Transfer In Elastico-Viscous Fluid Due To Nanoparticles, Where The Fluid Is Impinging Obliquely To The Stretchable Surface: A Numerical Study, Tariq Javed, Abuzar Ghaffari, Tasawar Hayat

Applications and Applied Mathematics: An International Journal (AAM)

This article addresses the two-dimensional oblique stagnation point flow of non-Newtonian fluid in the presence of nanoparticles. Constitutive equations of Walter-B fluid are employed in the mathematical development of the relevant problems. Mathematical formulation includes the Brownian motion and thermophoresis effects. The resulting nonlinear system of equations are analyzed through Chebyshev Spectral Newton Iterative Scheme (CSNIS). A comparative study of present results through tabular values has been made with the previous results in a limiting sense and an excellent agreement is noted. It is also found that in near stagnation point region, the heat transfer rate and mass diffusion flux …

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Priority Queueing System With A Single Server Serving Two Queues M[X1],M[X2]/G1,G2/1 With Balking And Optional Server Vacation, G. Ayyappan, P. Thamizhselvi Jun 2016

Priority Queueing System With A Single Server Serving Two Queues M[X1],M[X2]/G1,G2/1 With Balking And Optional Server Vacation, G. Ayyappan, P. Thamizhselvi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we study a vacation queueing system with a single server simultaneously dealing with an M[x1] /G1/1 and an M[x2] /G2/1 queues. Two classes of units, priority and non-priority, arrive at the system in two independent compound Poisson streams. Under a non-preemptive priority rule, the server provides a general service to the priority and non-priority units. We further assume that the server may take a vacation of random length just after serving the last customer in the priority unit present in the system. If the server …

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Analysis Of Incomplete Longitudinal Binary Data-A Combined Markov’S Transition And Logistic Model For Non-Ignorable Missingness, Francis Erebholo, Paul Bezandry, Victor Apprey, John Kwagyan Jun 2016

Analysis Of Incomplete Longitudinal Binary Data-A Combined Markov’S Transition And Logistic Model For Non-Ignorable Missingness, Francis Erebholo, Paul Bezandry, Victor Apprey, John Kwagyan

Applications and Applied Mathematics: An International Journal (AAM)

The problem of incomplete data is a common phenomenon in research that involves the longitudinal design approach. We investigate and develop a likelihood-based approach for incomplete longitudinal binary data using the disposition model when the missing value mechanism is non-ignorable. We combined Markov’s transition and a logistic regression model to build the dropout process and model the response using conditional logistic regression model. By holding the missingness parameter that is weakly identified constant, we analyzed their effects through a sensitivity analysis as the estimation of parameters in MLE for non-ignorable missing data is not generally plausible. An application of our …

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Measurement Error Estimation Methods In Survey Methodology, Alireza Zahedian, Roshanak A. Saba Jun 2016

Measurement Error Estimation Methods In Survey Methodology, Alireza Zahedian, Roshanak A. Saba

Applications and Applied Mathematics: An International Journal (AAM)

One of the most important topics that are discussed in survey methodology is the accuracy of statistics or survey errors that may occur in the parameters estimation process. In statistical literature, these errors are grouped into two main categories: sampling errors and non-sampling errors. Measurement error is one of the most important non-sampling errors. Since estimating of measurement error is more complex than other types of survey errors, much more research has been done on ways of preventing or dealing with this error. The main problem associated with measurement error is the difficulty to measure or estimate this error in …

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Stability Condition Of A Retrial Queueing System With Abandoned And Feedback Customers, Amina A. Bouchentouf, Abbes Rabhi, Lahcene Yahiaoui Dec 2015

Stability Condition Of A Retrial Queueing System With Abandoned And Feedback Customers, Amina A. Bouchentouf, Abbes Rabhi, Lahcene Yahiaoui

Applications and Applied Mathematics: An International Journal (AAM)

This paper deals with the stability of a retrial queueing system with two orbits, abandoned and feedback customers. Two independent Poisson streams of customers arrive to the system, and flow into a single-server service system. An arriving one of type i; i = 1; 2, is handled by the server if it is free; otherwise, it is blocked and routed to a separate type-i retrial (orbit) queue that attempts to re-dispatch its jobs at its specific Poisson rate. The customer in the orbit either attempts service again after a random time or gives up receiving service and leaves the system …

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An Optimal Reinsurance Contract From Insurer's And Reinsurer's Viewpoints, Ali P. Bazaz, Amir T. Payandeh Najafabadi Dec 2015

An Optimal Reinsurance Contract From Insurer's And Reinsurer's Viewpoints, Ali P. Bazaz, Amir T. Payandeh Najafabadi

Applications and Applied Mathematics: An International Journal (AAM)

This article constructs two classes of appropriate reinsurance contracts from both an insurer’s and a reinsurer’s viewpoints. The first class, say C; has been constructed by minimizing the conditional tail expectation, say CTE, of an insurer’s random risk. Then an optimal reinsurance contract has been obtained by estimating the reinsurance’s random risk, using the Bayesian estimation method while the second class of reinsurance contracts, say C*; is obtained by minimizing a convex combination of the CTE of both the insurer’s and reinsurer’s random risks. These two approaches consider both the insurer’s and reinsurer’s viewpoints to establish an optimal reinsurance contract. …

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An M/G/1 Queue With Server Breakdown And Multiple Working Vavation, S. P. Bala Murugan, K. Santhi Dec 2015

An M/G/1 Queue With Server Breakdown And Multiple Working Vavation, S. P. Bala Murugan, K. Santhi

Applications and Applied Mathematics: An International Journal (AAM)

This paper deals with the steady state behavior of an M=G=1 multiple working vacation queue with server breakdown. The server works with different service times rather than completely stopping service during a vacation. Both service times in a vacation period and in a regular service period are assumed to be generally distributed random variables. The system may breakdown at random and repair time is arbitrary. Further, just after completion of a customer’s service the server may take a multiple working vacation. Supplementary variable technique is employed to find the probability generating function for the number of customers in the system. …

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Analysis Of Repairable M[X]/(G1,G2)/1 - Feedback Retrial G-Queue With Balking And Starting Failures Under At Most J Vacations, P. Rajadurai, M. C. Saravanarajan, V. M. Chandrasekaran Dec 2015

Analysis Of Repairable M[X]/(G1,G2)/1 - Feedback Retrial G-Queue With Balking And Starting Failures Under At Most J Vacations, P. Rajadurai, M. C. Saravanarajan, V. M. Chandrasekaran

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we discuss the steady state analysis of a batch arrival feedback retrial queue with two types of service and negative customers. Any arriving batch of positive customers finds the server is free, one of the customers from the batch enters into the service area and the rest of them join into the orbit. The negative customer, arriving during the service time of a positive customer, will remove the positive customer in-service and the interrupted positive customer either enters into the orbit or leaves the system. If the orbit is empty at the service completion of each type …

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Generating Random Vectors Using Transformation With Multiple Roots And Its Applications, Qidi Peng, Henry Schellhorn, Lu Zhu Jun 2015

Generating Random Vectors Using Transformation With Multiple Roots And Its Applications, Qidi Peng, Henry Schellhorn, Lu Zhu

Applications and Applied Mathematics: An International Journal (AAM)

An approach is proposed to generate random vectors using transformation with multiple roots. This approach generalizes the one-dimensional inverse transformation with multiple roots method to higher dimensions, i.e., to random vectors with or without densities. In this approach, multiple roots of the transformation and probabilities of selecting each of the roots are derived. The strategies for constructing such a transformation are discussed and several examples are presented to motivate this simulation approach.

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A Note On An M/M/S Queueing System With Two Reconnect And Two Redial Orbits, Amina A. Bouchentouf, Hanane Sakhi Jun 2015

A Note On An M/M/S Queueing System With Two Reconnect And Two Redial Orbits, Amina A. Bouchentouf, Hanane Sakhi

Applications and Applied Mathematics: An International Journal (AAM)

A queueing system with two reconnect orbits, two redial (retrial) orbits, s servers and two independent Poisson streams of customers is considered. An arriving customer of type i, i = 1, 2 is handled by an available server, if there is any; otherwise, he waits in an infinite buffer queue. A waiting customer of type i who did not get connected to a server will lose his patience and abandon after an exponentially distributed amount of time, the abandoned one may leave the system (lost customer) or move into one of the redial orbits, from which he makes a new …

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