• Journal of applied mathematics & informatics
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• v.41 no.2
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• pp.449-468
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• 2023

This paper deals in the study of the estimation of the parameters of Erlang distribution based on rank set sampling and some of its modifications. Here we considered Maximum Likelihood (ML) and the Bayesian technique to estimate the shape and scale parameter of Erlang distribution based on RSS and its some modifications such as ERSS, MRSS, and MRSSu. The derivation for unknown parameters of Erlang distribution is well presented using normal approximation to the asymptotic distribution of ML estimators. But due to the complexity involves in the integral, the Bayes estimator of unknown parameters is obtained using MCMC method. Further, we compared the MSE of estimation in different sampling schemes with different set sizes and cycle size. A real-life data application is also given to illustrate the efficiency of the proposed scheme.

• Communications for Statistical Applications and Methods
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• v.14 no.1
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• pp.33-55
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• 2007

The economic world is full of patterns, many of which exert a profound influence over society and business. One of the most contentious is the distribution of wealth. Way back in 1897, an Italian engineer-turned-economist named Vilfredo Pareto discovered a pattern in the distribution of wealth that appears to be every bit as universal as the laws of thermodynamics or chemistry. The present paper proposes some Bayes estimators of shape parameter of Pareto income distribution in censored sampling. Asymmetric LINEX loss function has been considered to study the effects of overestimation and underestimation. For the prior distribution of the parameter involved a number of priors including one and two-parameter exponential, truncated Erlang and doubly truncated gamma have been contemplated to express the belief of the experimenter s/he has regarding the parameter. The estimators thus obtained have been compared theoretically and empirically with the corresponding estimators under squared error loss function, some of which were reported by Bhattacharya et al. (1999).

• Journal of Information Technology Services
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• v.10 no.4
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• pp.119-131
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• 2011

When your company buys packaged software, the company needs to determine how many software licenses must be purchased. If the quantity is too small, it will be not enough for the users to access the programs at anytime within the company. Conversely, if the quantity is too large, they will waste a lot of money. In this paper, we surveyed several number of researchers of K institute and derived the using pattern of a specific packaged software. We estimated a proper number of packaged software licenses by Erlang Loss Function, the Engset Model, and simulation model. With the results of the three methodologies, we were able to empirically verify economic benefits of packaged software purchase by comparing NPV (Net Present Value) between user licenses and network licenses. Consequently, TCO of user licenses is much higher than that of network licenses. We had probabilistically calculated proper number of licenses based on the using pattern of users. Hence, this paper will be useful for decision makers who are going to determine package software's type and quantity from an economic perspective.

• Journal of the Korean Operations Research and Management Science Society
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• v.21 no.2
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• pp.49-58
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• 1996

The generalized Erlang loss function, extensively studied in the literature, is revisited. We study the steady state loss probability in M/M/s/s + c queueing system and prove that it satisfies the first and second order properties in integral number of servers as well as integral queue capacities. Also we study the problem of allocating integral number of servers and queue capacities, and develop an algorithm to obtian an optimal allocation of them individually and jointly with the small number of computations.