# Probability Distributions

Distributions are some of the most important functions in statistics. They allow you to accurately model, describe and predict the probability of certain outcomes. This is why they are used in all sort of fields such as Statistical Inference, Data Analysis, Risk Assessment, Simulation and Modelling, Finance and Economics, Quality Control as well as Describing Uncertainty. Probability Distributions are also widely used in the development of Artificial Intelligence(AI).

## CDF Probability Distributions in MatDeck

PDF stands for Probability Density Function. It is a concept used in probability theory and statistics to describe the probability distribution of a continuous random variable.

• cauchydist
• chidist
• dblexponentialdist
• exponentionrialdist
• fdist
• geometricdist
• logarthmicdist
• normaldist
• poissondist
• tdist

## PDF Probability Distributions in MatDeck

CDF stands for Cumulative Distribution Function. It is a concept used in probability theory and statistics to describe the distribution of a random variable.

• cauchydens
• chidens
• dblexponentialdens
• exponentionrialdens
• fdens
• geometricdens
• logarthmicdens
• normaldens
• poissondens
• tdens

## Inverse Probability Distributions in MatDeck

MatDeck provides inverse cumulative distribution functions for all of its distributions, this allows for users to sample estimates from specific distributions, preform simulations and create models. Furthermore, it is used in statistical inference, Monte Carlo methods and numerical integration.

Below is a list of all MatDeck inverse cumulative distribution functions:

• Betainv
• Cauchyinv
• Chiinv
• Dblexponentialinv
• Exponentionrialinv
• Finv
• Gammainv
• Geometricinv
• Logarthmicinv
• Normalinv
• Poissoninv
• Tinv

## MatDeck Statistical Library alongside Probability Distributions

Regression Analysis can be efficiently performed in MatDeck using functions such as regression, regressiontable, and curveregtable. MatDeck’s Regression Analysis Functions are designed to provide quick and easy access to results, enabling you to draw precise conclusions based on concise and accurate data. With the available functions, like regressiontable, you can identify the most suitable regression for your data without the need to individually test and execute multiple regressions. By utilizing regressiontable, you can obtain all the necessary answers in a single line of code.

Probability density is a fundamental concept in probability theory and statistics that describes the likelihood of a random variable taking on a particular value within a given range. It is commonly used to represent continuous random variables and is often denoted by a probability density function (PDF).

Standard deviation and variance are measures of data dispersion, providing information about how spread out the data points are around the mean. Variance calculates the average squared deviation of each data point from the mean, while standard deviation is the square root of the variance. Autocorrelation, on the other hand, measures the statistical relationship between observations at different time points in a time series, indicating the extent to which current values are related to past values. Autocorrelation helps identify patterns and dependencies in the data All of this is packaged into simple functions with MatDeck.

### Random Number Generators are:

• betarandnum – Random number created with Beta distribution
• betarandvec – Vector of random numbers created with Beta distribution
• betarandmat – Matrix of random numbers created with Beta distribution
• cauchyrandnum – Random number created with Cauchy distribution
• cauchyrandvec – Vector of random numbers created with Cauchy distribution
• cauchyrandmat – Matrix of random numbers created with Cauchy distribution
• chi2randnum – Random number created with Chi square distribution
• chi2randvec – Vector of random numbers created with Chi square distribution
• chi2randmat – Matrix of random numbers created with Chi square distribution
• dblexprandnum – Random number created with Double Exponential distribution
• dblexprandvec – Vector of random numbers created with Double Exponential distribution
• dblexprandmat – Matrix of random numbers created with Double Exponential distribution
• exprandnum – Random number created with Exponential distribution