Add to ORKGThe computer algebra system, MathematicaTM, is used to determine the exact distributions for sums and means of small random samples taken from a specific probability density function. The method used is the Inverse Laplace Transform for real-valued functions. These distributions are used to compare exact probabilities for probability interval statements for sums and means with normal approximations for these probabilities using the Central Limit Theorem. The maximum normal approximation errors are determined for probability intervals for various sample sizes
As the number of samples from a normal probability distribution with a user-defined mean and user-de...
We derive the Edgeworth expansion to order n-1 of the cumulative distribution function of the studen...
Estimation of probabilities from empirical data samples has drawn close attention in the scientific ...
The computer algebra system, MathematicaTM, is used to determine the exact distributions for sums an...
This Mathematica demonstration compares the sample uniform probability distribution with the theoret...
This paper considers the problem of finding the exact distribution and exact moments of the median o...
The triangular distribution is used in discrete-event and Monte Carlo simulation as a key probabilit...
Nous introduisons une nouvelle méthode pour approximer la distribution de variables aléatoires. L'ap...
The most important properties of normal and Student t-distributions are presented. A number of appli...
The principal objective of this study has been to derive and develop algorithms to approximate proba...
This note proposes a tool to investigate and demonstrate the adequacy of the central limit theorem i...
In the paper, we discuss the transformation of the asymptotic expansion for the distribution of a st...
We show how to use computer algebra for computing exact distributions on nonparametric statistics. W...
AbstractExact bounds for the mean value of a fractional moment, such as the sample standard deviatio...
It is argued that an integral part of the process by which the results of small sample theory can be...
As the number of samples from a normal probability distribution with a user-defined mean and user-de...
We derive the Edgeworth expansion to order n-1 of the cumulative distribution function of the studen...
Estimation of probabilities from empirical data samples has drawn close attention in the scientific ...
The computer algebra system, MathematicaTM, is used to determine the exact distributions for sums an...
This Mathematica demonstration compares the sample uniform probability distribution with the theoret...
This paper considers the problem of finding the exact distribution and exact moments of the median o...
The triangular distribution is used in discrete-event and Monte Carlo simulation as a key probabilit...
Nous introduisons une nouvelle méthode pour approximer la distribution de variables aléatoires. L'ap...
The most important properties of normal and Student t-distributions are presented. A number of appli...
The principal objective of this study has been to derive and develop algorithms to approximate proba...
This note proposes a tool to investigate and demonstrate the adequacy of the central limit theorem i...
In the paper, we discuss the transformation of the asymptotic expansion for the distribution of a st...
We show how to use computer algebra for computing exact distributions on nonparametric statistics. W...
AbstractExact bounds for the mean value of a fractional moment, such as the sample standard deviatio...
It is argued that an integral part of the process by which the results of small sample theory can be...
As the number of samples from a normal probability distribution with a user-defined mean and user-de...
We derive the Edgeworth expansion to order n-1 of the cumulative distribution function of the studen...
Estimation of probabilities from empirical data samples has drawn close attention in the scientific ...