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A microbiology application of the skew-Laplace distribution.

Olga Julià, Josep Vives-Rego (2008)


Flow cytometry scatter are ofen used in microbiology, and their measures are related to bacteria size and granularity. We present an application of the skew-Laplace distribution to flow cytometry data. The goodness of fit is evaluated both graphically and numerically. We also study skewness and kurtosis values to assess usefulness of the skew-Laplace distribution.

A new family of compound lifetime distributions

A. Asgharzadeh, Hassan S. Bakouch, Saralees Nadarajah, L. Esmaeili (2014)


In this paper, we introduce a general family of continuous lifetime distributions by compounding any continuous distribution and the Poisson-Lindley distribution. It is more flexible than several recently introduced lifetime distributions. The failure rate functions of our family can be increasing, decreasing, bathtub shaped and unimodal shaped. Several properties of this family are investigated including shape characteristics of the probability density, moments, order statistics, (reversed) residual...

A new weighted Gompertz distribution with applications to reliability data

Hassan S. Bakouch, Ahmed M. T. Abd El-Bar (2017)

Applications of Mathematics

A new weighted version of the Gompertz distribution is introduced. It is noted that the model represents a mixture of classical Gompertz and second upper record value of Gompertz densities, and using a certain transformation it gives a new version of the two-parameter Lindley distribution. The model can be also regarded as a dual member of the log-Lindley- X family. Various properties of the model are obtained, including hazard rate function, moments, moment generating function, quantile function,...

A Note on Computing Extreme Tail Probabilities of the Noncentral t -Distribution with Large Noncentrality Parameter

Viktor Witkovský (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The noncentral t -distribution is a generalization of the Student’s t -distribution. In this paper we suggest an alternative approach for computing the cumulative distribution function (CDF) of the noncentral t -distribution which is based on a direct numerical integration of a well behaved function. With a double-precision arithmetic, the algorithm provides highly precise and fast evaluation of the extreme tail probabilities of the noncentral t -distribution, even for large values of the noncentrality...

A second order approximation for the inverse of the distribution function of the sample mean

Jorge M. Arevalillo (2001)


The classical quantile approximation for the sample mean, based on the central limit theorem, has been proved to fail when the sample size is small and we approach the tail of the distribution. In this paper we will develop a second order approximation formula for the quantile which improves the classical one under heavy tails underlying distributions, and performs very accurately in the upper tail of the distribution even for relatively small samples.

A study of the tangent space model of the von Mises-Fisher distrubution.

A. Chakak, L. Imhali (2003)


For a random rotation X = M0 eφ(ε) where M0 is a 3 x 3 rotation, ε is a trivariate random vector, and φ(ε) is a skew symmetric matrix, the least squares criterion consists of seeking a rotation M called the mean rotation minimizing tr[(M - E(X))t (M - E(X))]. Some conditions on the distribution of ε are set so that the least squares estimator is unbiased. Of interest is when ε is normally distributed N(0;Σ). Unbiasedness of the least squares estimator is dealt with according to eigenvalues of Σ.

Angles de droits et de revers. Distribution circulaire

C. Carcassonne (1974)

Mathématiques et Sciences Humaines

Dans cet article, on traite un échantillon d'angles de droits et de revers de pièces de monnaies. On a cherché à en donner une description statistique correcte et à ajuster une loi théorique puis à construire un test d'homogénéité non paramétrique de deux échantillons distribués sur le cercle.

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