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Probability Distributions01:32

Probability Distributions

The probability of a random variable x  is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson probability...
Distributions to Estimate Population Parameter01:26

Distributions to Estimate Population Parameter

The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
Binomial Probability Distribution01:15

Binomial Probability Distribution

A binomial distribution is a probability distribution for a procedure with a fixed number of trials, where each trial can have only two outcomes.
The outcomes of a binomial experiment fit a binomial probability distribution. A statistical experiment can be classified as a binomial experiment if the following conditions are met:
There are a fixed number of trials. Think of trials as repetitions of an experiment. The letter n denotes the number of trials.
There are only two possible outcomes,...
Probability Histograms01:17

Probability Histograms

A probability histogram is a visual representation of a probability distribution. Similar a typical histogram, the probability histogram consists of contiguous (adjoining) boxes. It has both a horizontal axis and a vertical axis. The horizontal axis is labeled with what the data represents. The vertical axis is labeled with probability. Each rectangular bar in the histogram is 1 unit wide, which suggests that the area under each bar equals the probability, P(x), where x is 1, 2, 3, and so on.
Sampling Distribution01:12

Sampling Distribution

Given simple random samples of size n from a given population with a measured characteristic such as mean, proportion, or standard deviation for each sample, the probability distribution of all the measured characteristics is called a sampling distribution. How much the statistic varies from one sample to another is known as the sampling variability of a statistic. You typically measure the sampling variability of a statistic by its standard error. The standard error of the mean is an example...
Parametric Survival Analysis: Weibull and Exponential Methods01:14

Parametric Survival Analysis: Weibull and Exponential Methods

Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...

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Related Experiment Video

Updated: Jun 24, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Simulating multivariate g-and-h distributions.

Rhonda K Kowalchuk1, Todd C Headrick

  • 1Southern Illinois University Carbondale, Illinois, USA. rkowal@siu.edu

The British Journal of Mathematical and Statistical Psychology
|April 11, 2009
PubMed
Summary
This summary is machine-generated.

This study introduces a new method for generating multivariate g-and-h distribution data with specific correlations. This addresses a gap in modeling complex real-world datasets using the Tukey g-and-h family.

Related Experiment Videos

Last Updated: Jun 24, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Area of Science:

  • Statistics
  • Probability Theory
  • Data Science

Background:

  • The Tukey g-and-h distribution is valuable for univariate data modeling.
  • Existing research lacks methods for multivariate g-and-h data generation with controlled correlations.

Purpose of the Study:

  • To extend the Tukey g-and-h distribution to multivariate settings.
  • To develop a methodology for generating multivariate g-and-h data with specified correlations.

Main Methods:

  • Development of novel methodology for multivariate g-and-h distribution.
  • Implementation of algorithms in Mathematica 7.0 for data generation.
  • Monte Carlo simulation to validate the proposed methodology.

Main Results:

  • Successful extension of the g-and-h family to multivariate data generation.
  • Demonstration of generating multivariate g-and-h data with specified correlations.
  • Validation of the methodology through simulation and a practical example.

Conclusions:

  • The presented methodology effectively enables multivariate g-and-h data generation with specified correlations.
  • This work fills a critical gap in statistical modeling for complex datasets.
  • Algorithms are available to facilitate the practical application of these methods.