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Journal Cover   International Journal of Advanced Statistics and Probability
  [3 followers]  Follow
  This is an Open Access Journal Open Access journal
   ISSN (Print) 2307-9045 - ISSN (Online) 2307-9045
   Published by Science Publishing Corporation Homepage  [12 journals]
  • A note on a new class of generalized Pearson distribution arising from
           Michaelis-Menten function of enzyme kinetics

    • Authors: Mohammad Shakil, Jai Narain Singh
      Pages: 25 - 34
      Abstract: Many problems of enzyme kinetics can be described by a function known as the Michaelis-Menten (M-M) function. In this paper, motivated by the importance of Michaelis-Menten function in biochemistry and other biological phenomena, we have introduced a new class of generalized Pearson distribution arising from Michaelis-Menten function. Various properties of this distribution are derived, for example, its probability density function (pdf), cumulative distribution function (cdf), moment, entropy function, and relationships with some well-known continuous probability distributions. The graphs of the pdf and cdf of our new distribution are provided for some selected values of the parameters. It is observed that our new distribution is positively skewed and unimodal. We hope that the findings of this paper will be useful in many applied research problems. 2000 Mathematics Subject Classification: 60E05, 62E10, 62E15.
      PubDate: 2015-01-02
      Issue No: Vol. 3, No. 1 (2015)
  • Stochastic differential equations and comparison of financial models with
           levy process using Markov chain Monte Carlo (MCMC) simulation

    • Authors: Kianoush Fathi Vajargah
      Pages: 35 - 42
      Abstract: An available method of modeling and predicting the economic time series is the use of stochastic differential equations, which are often determined as jump-diffusion stochastic differential equations in financial markets and underlier economic dynamics. Besides the diffusion term that is a geometric Brownian model with Wiener random process, these equations contain a jump term that follows Poisson process and depends on the type of market. This study presented two different models based on a certain class of jump-diffusion stochastic differential equations with random fluctuations: Black- Scholes model and Merton model (1976), including jump-diffusion (JD) model, which were compared, and their parameters and hidden variables were evaluated using Markov chain Monte Carlo (MCMC) method.
      PubDate: 2015-01-25
      Issue No: Vol. 3, No. 1 (2015)
  • Bayesian estimation based on generalized order statistics from
           exponentiated Weibull Poisson model

    • Authors: Abd-Elfattah A. M, Amal S. Hassan, Said G. Nassr
      Pages: 43 - 52
      Abstract: In this research paper, the estimation of the unknown parameters for the exponentiated Weibull Poisson distribution using the concept of generalized order statistics is investigated from Bayesian approach. The squared error, LINEX and general entropy loss functions are considered for Bayesian computation.  Bayes estimates based on Progressively type II censored and the joint density function of ordinary order statistics are considered as special cases of generalized order statistics. Finally simulation study is conducted for illustrative purposes.
      PubDate: 2015-03-14
      Issue No: Vol. 3, No. 1 (2015)
  • The Transmuted Inverse Exponential Distribution

    • Authors: Pelumi Oguntunde, Olusola Adejumo
      Pages: 1 - 7
      Abstract: This article introduces a two-parameter probability model which represents another generalization of the Inverse Exponential distribution by using the quadratic rank transmuted map. The proposed model is named Transmuted Inverse Exponential (TIE) distribution and its statistical properties are systematically studied. We provide explicit expressions for its moments, moment generating function, quantile function, reliability function and hazard function. We estimate the parameters of the TIE distribution using the method of maximum likelihood estimation (MLE). The hazard function of the model has an inverted bathtub shape and we propose the usefulness of the TIE distribution in modeling breast cancer and bladder cancer data sets.
      PubDate: 2014-12-12
      Issue No: Vol. 3, No. 1 (2014)
  • Determining the optimum confidence interval based on the hybrid Monte
           Carlo method and its application in financial calculations

    • Authors: Kianoush Fathi Vajargah
      Pages: 8 - 14
      Abstract: The accuracy of Monte Carlo and quasi-Monte Carlo methods decreases in problems of high dimensions. Therefore, the objective of this study was to present an optimum method to increase the accuracy of the answer. As the problem gets larger, the resulting accuracy will be higher. In this respect, this study combined the two previous methods, QMC and MC, and presented a hybrid method with efficiency higher than that of those two methods.
      PubDate: 2014-12-15
      Issue No: Vol. 3, No. 1 (2014)
  • Evaluating system reliability using linear-exponential distribution

    • Authors: Ghasem Ezzati, Abbas Rasouli
      Pages: 15 - 24
      Abstract: Safety is a main criterion to design every system. Among various theories, which are applied to improve system safety, reliability theory is known as a powerful tool to reach higher safety levels in system design. In this paper, a compound of series and parallel systems is considered for reliability improvement. This system includes three items that two items are connected in parallel and their compound item is connected to the third item in series. It's assumed that the items are independent and their longevity follows linear-exponential distribution function. Reliability function of the mentioned system is formulated using linear-exponential distribution function. Then, three improvement methods will be applied to enhance system reliability. In each method, different sets of items will be considered for improvement and their reliability functions will be reformulated. A data analysis will be done in order to compare different improvement methods and a conclusion will be made based on the analyzed data.
      PubDate: 2014-12-19
      Issue No: Vol. 3, No. 1 (2014)
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