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Journal Cover   International Journal of Advanced Statistics and Probability
  [1 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)
  • Fast online detection of outliers using least-trimmed squares regression
           with non-dominated sorting based initial subsets

    • Authors: Mehmet Hakan Satman
      Pages: 53 - 63
      Abstract: In this paper, a new algorithm is devised for calculating the Least Trimmed of Squares (LTS) estimator. The algorithm consists of two steps. In the first step, the non-dominated sorting algorithm is applied on the design matrix of regression data for selecting a clean subset of observations. In the second step, C-steps are iterated to adjust the LTS estimators. The algorithm is fast and precise for small sample sizes, however, the sorting algorithm is computationally inefficient in large datasets. A fast update mechanism can be used in online data with a linear increase in computation time. Some properties of the sorting algorithm are also investigated under some transformations. Results of applying the algorithm on some well-known datasets and Monte Carlo simulations show that the proposed algorithm is suitable to use in many cases when the computation time is the major objective and a moderate level of precision is enough.
      PubDate: 2015-04-04
      Issue No: Vol. 3, No. 1 (2015)
  • Analysis of deaths in a Nigerian hospital: the case of Federal Medical
           Centre (FMC), Umuahia

    • Authors: Emmanuel Ekpenyong, Iheanyi Emenike
      Pages: 64 - 71
      Abstract: A Poisson regression model was fitted to the causes of death in Federal Medical Center (FMC), Umuahia. The basic violation of the model which is over-dispersion was confirmed absent with the use of a plot of residual against fitted values, the Pearson statistics and the comparison of the log-likelihoods of the Poisson regression and Negative Binomial regression models. Diseases affecting the excretory and neurological systems respectively were found to be insignificant in the model, while the rest of the other causes of deaths – were found to be significant in the model at 5% level of significance. The leading causes of death in the hospital were determined to be diseases affecting the digestive and circulatory system, injuries, endocrine and neonatal related diseases, and cancers.
      PubDate: 2015-04-17
      Issue No: Vol. 3, No. 1 (2015)
  • Constant-stress partially accelerated life tests for inverted Weibull
           distribution with multiple censored data

    • Authors: Amal S. Hassan, Salwa M. Assar, Ahmed N. Zaky
      Pages: 72 - 82
      Abstract: Testing the lifetime of items under normal use condition often requires a long period of time, especially for products having high reliability. To minimize the costs involved in testing without reducing the quality of the data obtained, the items run at higher than usual level of stresses to induce early failures in a short time. This article concerns with constant–stress partially accelerated life test with multiple censored data. The life time of test item is assumed to follow inverted Weibull distribution. Maximum likelihood estimates are obtained for the model parameters and acceleration factor. In addition, asymptotic variance and covariance matrix of the estimators is given. The confidence intervals of the unknown parameters and acceleration factor are constructed for large sample sizes. Simulation studies are performed to investigate the performance of the estimators.
      PubDate: 2015-04-25
      Issue No: Vol. 3, No. 1 (2015)
  • On the skewed sinh-normal distribution

    • Authors: S. K. Ashour, Ahmed Saad
      Pages: 83 - 92
      Abstract: Leiva et al. [10] introduce the skewed sinh-normal distribution, which is a skewed version of the sinh-normal distribution, discussed some of its properties and characterized an extension of the Birnbaum–Saunders distribution associated with this distribution. In this paper, we will introduce further properties of the skewed sinh-normal distribution, and introduce a new approximate form of its probability density function and cumulative distribution function (cdf), along with numerical comparison between the exact and approximate values of its cdf. Moreover, a random number generator for the distribution will be suggested and a goodness of fit test will be carried out to examine the effectiveness of the proposed random number generator. Finally, maximum likelihood estimation for the unknown parameter of the skewed sinh-normal distribution will be investigated, and numerical illustration for the new results will be discussed.
      PubDate: 2015-05-08
      Issue No: Vol. 3, No. 1 (2015)
  • Performance analysis on least absolute shrinkage selection operator,
           elastic net and correlation adjusted elastic net regression methods

    • Authors: Pascalis Kadaro Matthew, Abubakar Yahaya
      Pages: 93 - 99
      Abstract: Some few decades ago, penalized regression techniques for linear regression have been developed specifically to reduce the flaws inherent in the prediction accuracy of the classical ordinary least squares (OLS) regression technique. In this paper, we used a diabetes data set obtained from previous literature to compare three of these well-known techniques, namely: Least Absolute Shrinkage Selection Operator (LASSO), Elastic Net and Correlation Adjusted Elastic Net (CAEN). After thorough analysis, it was observed that CAEN generated a less complex model.
      PubDate: 2015-05-16
      Issue No: Vol. 3, No. 1 (2015)
  • Characterizations of continuous probability distributions occurring in
           physics and allied sciences by truncated moment

    • Authors: Mohammad Ahsanullah, Mohammad Shakil
      Pages: 100 - 114
      Abstract: A probability distribution can be characterized through various methods. Before a particular probability distribution model is applied to fit the real-world data, it is necessary to confirm whether the given continuous probability distribution satisfies the underlying requirements by its characterization. In this paper, characterizations of some continuous probability distributions occurring in physics and allied sciences have been established. We have considered the normal, Laplace, Lorentz, logistic, Boltzmann, Rayleigh, log-normal, Maxwell, Fermi-Dirac, and Bose-Einstein distributions, and characterized them by applying a truncated moment method; that is, by taking a product of reverse hazard rate and another function of the truncated point. It is hoped that the proposed characterizations will be useful for researchers in various fields of physics and allied sciences.
      PubDate: 2015-05-24
      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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