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Journal Cover International Journal of Advanced Statistics and Probability
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  This is an Open Access Journal Open Access journal
     ISSN (Print) 2307-9045 - ISSN (Online) 2307-9045
     Published by Science Publishing Corporation Homepage  [11 journals]
  • Estimation of the Parameters of the Bivariate Generalized Exponential
           Distribution using Accelerated Life Testing with Censoring Data

    • Authors: Salwa Asser, Mary Abd EL-Maseh
      Abstract: In this paper, the estimation for the bivariate generalized exponential (BVGE) distribution under type-I censored with constant stress accelerated life testing (CSALT) are discussed. The scale parameter of the lifetime distribution at constant stress levels is assumed to be an inverse power law function of the stress level. The unknown parameters are estimated by the maximum likelihood approach and their approximate variance-covariance matrix is obtained. Then, the numerical studies are introduced to illustrate the approach study using samples which have been generated from the bivariate generalized exponential distribution. Keywords: Accelerated life testing, Bivariate generalized exponential distribution, Constant stress, Type-I censoring, Maximum likelihood estimation.
      PubDate: 2014-08-18
      Issue No: Vol. 2 (2014)
  • Construction of second order slope rotatable designs under tri-diagonal
           correlated structure of errors using central composite designs

    • Authors: Rajyalakshmi kottapalli, B. Re. Victorbabu
      Abstract: In this paper, second order slope rotatable design (SOSRD) under tri-diagonal correlated structure of errors using central composite designs (CCD) is suggested. Keywords: Response Surface Designs, Rotatable Designs, Slope Rotatable Designs, Second Order Slope Rotatable Designs (SOSRD), Tri-Diagonal Correlated Errors.
      PubDate: 2014-07-15
      Issue No: Vol. 2 (2014)
  • Neyman’s causal model with stochastic potential outcomes:
           implications for the completely randomized design

    • Authors: Emil Scosyrev
      Abstract: In Neyman’s causal model (NCM), each subject participating in a two-arm randomized trial has a pair of potential outcomes – one outcome would be observed under treatment and another under control. In the stochastic version of NCM the two potential outcomes are viewed as possibly non-degenerate random variables with finite expectations and variances. The subject-level treatment effect is the expected outcome under treatment minus that under control, and the average treatment effect is the arithmetic mean of the subject-level effects. In the present paper properties of the ordinary “difference of means” estimator and its associated variance estimator are examined in the completely randomized design with stochastic potential outcomes. Estimation theory is developed under randomization distribution without commitment to any particular probability model for enrollment, because in real trials subjects are not enrolled by a sampling mechanism with known selection probabilities. It is shown that in this theoretical framework, the “difference of means” estimator is asymptotically normal and consistent for the average treatment effect in the study cohort, while its associated variance estimator is conservative, producing confidence intervals with at least nominal asymptotic coverage. The proofs are not trivial because in the randomization framework sample means under treatment and control are correlated random variables. Keywords: Causality; Clinical Trials; Internal Validity; Neyman’s Causal Model; Randomization-Based Inference; Stochastic Potential Outcomes.
      PubDate: 2014-07-15
      Issue No: Vol. 2 (2014)
  • Comparison of resampling method applied to censored data

    • Authors: Claude Arrabal, Karina Silva, Ricardo Rocha, Ricardo Nonaka, Silvana Meira
      Abstract: This paper is about a comparison study among the performances of variance estimators of certain parameters, usingresampling techniques such as bootstrap and jackknife. The comparison will be made among several situations ofsimulated censored data, relating the observed values of estimates to real values. For real data, it will be consideredthe dataset Stanford heart transplant, analyzed by Cho et al. (2009) using the model of Cox regression (Cox, 1972)for adjustment. It is noted that the Jackknife residual is ecient to analyze inuential data points in the responsevariable. Keywords: bootstrap, Jackknife, simulation, Cox Regression Model, censored data.
      PubDate: 2014-06-05
      Issue No: Vol. 2 (2014)
  • Is there an absolutely continuous random variable with equal probability
           density and cumulative distribution functions in its support' Is it
           unique' What about in the discrete case'

    • Authors: Ernesto Veres-Ferrer, JoseM Pavia
      Abstract: This paper inquires about the existence and uniqueness of a univariate continuous random variable for which both cumulative distribution and density functions are equal and asks about the conditions under which a possible extrapolation of the solution to the discrete case is possible. The issue is presented and solved as a problem and allows to obtain a new family of probability distributions. The different approaches followed to reach the solution could also serve to warn about some properties of density and cumulative functions that usually go unnoticed, helping to deepen the understanding of some of the weapons of the mathematical statistician’s arsenal. Keywords: Cumulative Distribution Function; Density Function; Elasticity; Mathematical Statistics; Reversed Hazard Rate.
      PubDate: 2014-06-02
      Issue No: Vol. 2 (2014)
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