863,954 research outputs found
The Beta-Gompertz Distribution
In this paper, we introduce a new four-parameter generalized version of the
Gompertz model which is called Beta-Gompertz (BG) distribution. It includes
some well-known lifetime distributions such as beta-exponential and generalized
Gompertz distributions as special sub-models. This new distribution is quite
flexible and can be used effectively in modeling survival data and reliability
problems. It can have a decreasing, increasing, and bathtub-shaped failure rate
function depending on its parameters. Some mathematical properties of the new
distribution, such as closed-form expressions for the density, cumulative
distribution, hazard rate function, the th order moment, moment generating
function, Shannon entropy, and the quantile measure are provided. We discuss
maximum likelihood estimation of the BG parameters from one observed sample and
derive the observed Fisher's information matrix. A simulation study is
performed in order to investigate this proposed estimator for parameters. At
the end, in order to show the BG distribution flexibility, an application using
a real data set is presented.Comment: http://www.emis.de/journals/RCE/ingles/v37_1.htm
The right tail exponent of the Tracy-Widom-beta distribution
The Tracy-Widom beta distribution is the large dimensional limit of the top
eigenvalue of beta random matrix ensembles. We use the stochastic Airy operator
representation to show that as a tends to infinity the tail of the Tracy Widom
distribution satisfies P(TW_beta > a) = a^(-3/4 beta+o(1)) exp(-2/3 beta
a^(3/2))
The Index Distribution of Gaussian Random Matrices
We compute analytically, for large N, the probability distribution of the
number of positive eigenvalues (the index N_{+}) of a random NxN matrix
belonging to Gaussian orthogonal (\beta=1), unitary (\beta=2) or symplectic
(\beta=4) ensembles. The distribution of the fraction of positive eigenvalues
c=N_{+}/N scales, for large N, as Prob(c,N)\simeq\exp[-\beta N^2 \Phi(c)] where
the rate function \Phi(c), symmetric around c=1/2 and universal (independent of
), is calculated exactly. The distribution has non-Gaussian tails, but
even near its peak at c=1/2 it is not strictly Gaussian due to an unusual
logarithmic singularity in the rate function.Comment: 4 pages Revtex, 4 .eps figures include
The Beta Generalized Exponential Distribution
We introduce the beta generalized exponential distribution that includes the
beta exponential and generalized exponential distributions as special cases. We
provide a comprehensive mathematical treatment of this distribution. We derive
the moment generating function and the th moment thus generalizing some
results in the literature. Expressions for the density, moment generating
function and th moment of the order statistics also are obtained. We discuss
estimation of the parameters by maximum likelihood and provide the information
matrix. We observe in one application to real data set that this model is quite
flexible and can be used quite effectively in analyzing positive data in place
of the beta exponential and generalized exponential distributions
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