Integral transforms of the lognormal distribution are of great importance in statistics and probability, yet closed-form expressions do not exist. A wide variety of methods have been employed to provide approximations, both analytical and numerical. In this paper, we analyse a closed-form approximation (Formula presented.) of the Laplace transform (Formula presented.) which is obtained via a modified version of Laplace’s method. This approximation, given in terms of the Lambert W(⋅) function, is tractable enough for applications. We prove that ~(θ) is asymptotically equivalent to ℒ(θ) as θ → ∞. We apply this result to construct a reliable Monte Carlo estimator of ℒ(θ) and prove it to be logarithmically efficient in the rare event sense as θ...
This paper considers the problem of estimating probabilities of the form P (Y = w), for a given valu...
A simple and novel method is presented to approximate by the lognormal distribution the probability ...
A simple and novel method is presented to approximate the distribution of the sum of independent, bu...
In this review, we will consider two closely related problems associated with the lognormal distribu...
In this paper, the lognormal distribution is studied, and a new series representation is proposed. T...
It is shown that, when expressing arguments in terms of their logarithms, the Laplace transform of a...
Let (X-1, . . , X-n) be multivariate normal, with mean vector mu and covariance matrix Sigma, and le...
Abstract—Sums of lognormal random variables (RVs) are of wide interest in wireless communications an...
In this paper, we perform the computation of the Laplace-Stieljes transform of Lognormal and Weibull...
A random variable Y is said to have the Laplace distribution or the double exponential distribution ...
The normal-Laplace (NL) distribution results from convolving independent normally distributed and La...
Finding the distribution of the sum of lognormal random variables is an important mathematical probl...
The sum of the lognormal distributions is widely used for performance analysis in various areas, inc...
The calculation of the mean difference for the lognormal distribution involves several hard integral...
Logtype distributions were studied by a number of authors. Galton (1879) introduced log normal distr...
This paper considers the problem of estimating probabilities of the form P (Y = w), for a given valu...
A simple and novel method is presented to approximate by the lognormal distribution the probability ...
A simple and novel method is presented to approximate the distribution of the sum of independent, bu...
In this review, we will consider two closely related problems associated with the lognormal distribu...
In this paper, the lognormal distribution is studied, and a new series representation is proposed. T...
It is shown that, when expressing arguments in terms of their logarithms, the Laplace transform of a...
Let (X-1, . . , X-n) be multivariate normal, with mean vector mu and covariance matrix Sigma, and le...
Abstract—Sums of lognormal random variables (RVs) are of wide interest in wireless communications an...
In this paper, we perform the computation of the Laplace-Stieljes transform of Lognormal and Weibull...
A random variable Y is said to have the Laplace distribution or the double exponential distribution ...
The normal-Laplace (NL) distribution results from convolving independent normally distributed and La...
Finding the distribution of the sum of lognormal random variables is an important mathematical probl...
The sum of the lognormal distributions is widely used for performance analysis in various areas, inc...
The calculation of the mean difference for the lognormal distribution involves several hard integral...
Logtype distributions were studied by a number of authors. Galton (1879) introduced log normal distr...
This paper considers the problem of estimating probabilities of the form P (Y = w), for a given valu...
A simple and novel method is presented to approximate by the lognormal distribution the probability ...
A simple and novel method is presented to approximate the distribution of the sum of independent, bu...