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Skewness and the Beta Distribution
Journal of the Operational Research Society, 1990In this paper, alternative methods for estimating the beta distribution are proposed that utilize more information than the standard method based on the best, worst and most likely estimates. In particular, it is shown how information on skewness or the decision-maker's level of confidence can be incorporated into the estimation process.
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PERT and the beta distribution
IEEE Transactions on Engineering Management, 1967After reviewing the beta distribution and its properties, a simple technique is described for obtaining exact solutions to the cubic equation which results from the PERT constraint on standard deviation. These solutions are then used, together with the expression for the mode of the beta distribution, to determine graphically the specific values of the
William J. Mcbride +1 more
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Sankhya B, 2014
A new family of skewed distributions referred to as modified beta distributions is presented. Some properties of the new family including estimation procedures are derived. A real data application as well as simulation studies are described to show superior performance versus known models.
Shou Hsing Shih +2 more
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A new family of skewed distributions referred to as modified beta distributions is presented. Some properties of the new family including estimation procedures are derived. A real data application as well as simulation studies are described to show superior performance versus known models.
Shou Hsing Shih +2 more
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Robust project management with the tilted beta distribution
, 2015Recent years have seen an increase in the development of robust approaches for stochastic project management methodologies such as PERT (Program Evaluation and Review Technique).
Eugene D. Hahn +1 more
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Statistics & Probability Letters, 2003
Abstract The Dirichlet distribution is often used as a prior distribution for the parameters of a multinomial distribution. Because this distribution has support on the simplex 0⩽ x i ⩽1, ∑ x i =1, it does not serve as the prior for a correlated binomial distribution.
Ingram Olkin, Ruixue Liu
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Abstract The Dirichlet distribution is often used as a prior distribution for the parameters of a multinomial distribution. Because this distribution has support on the simplex 0⩽ x i ⩽1, ∑ x i =1, it does not serve as the prior for a correlated binomial distribution.
Ingram Olkin, Ruixue Liu
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The beta modified Weibull distribution
Lifetime Data Analysis, 2010A five-parameter distribution so-called the beta modified Weibull distribution is defined and studied. The new distribution contains, as special submodels, several important distributions discussed in the literature, such as the generalized modified Weibull, beta Weibull, exponentiated Weibull, beta exponential, modified Weibull and Weibull ...
Gauss M. Cordeiro +2 more
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, 2013
type="main"> There are three reasons why estimation of parametric income distributions may be useful when empirical data and estimators are available: to stabilize estimation; to gain insight into the relationships between the characteristics of the ...
Monique Graf, D. Nedyalkova
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type="main"> There are three reasons why estimation of parametric income distributions may be useful when empirical data and estimators are available: to stabilize estimation; to gain insight into the relationships between the characteristics of the ...
Monique Graf, D. Nedyalkova
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An asymptotic distribution of a specific beta distribution
International Conference on Automatic Control and Artificial Intelligence (ACAI 2012), 2012The asymptotic distribution of the Beta distribution is studied by means of decomposing the Beta distribution properly and the classical analysis is truncation method. It is proved that the asymptotic distribution of the Beta distribution is normal distribution when the two parameters a and b of the Beta distribution are all positive members and a over
Xiangdong Song +2 more
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The complementary beta distribution
Journal of Statistical Planning and Inference, 2002The complementary beta distribution is proposed as a new distribution on the unit interval. It results from reversing the roles of the distribution and quantile functions of the beta distribution. It has some attractive properties that are complementary to those of the beta distribution.
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