Distributions
Overview
Distributions are functions that specify how likely various outcomes
of a
random variable
are.
Functional Representations
Distributions are specified by a set of functions which can be used to determine the probability of any event using the
standard techniques of
analysis.
Distributions
- Bernoulli :
represents a random variable that can only take one of two values, a coin flip for example
- Beta :
a distribution that can only take values between 0 and1.
- Chi Square :
derived from the normal distribution and used frequently in statistical inference.
- Compound Poisson :
- Exponential :
The exponential distribution is usually used to model the length of time between events in a Poisson process.
- F Distribution :
often used in hypothese testing.
- Gamma :
- Lognormal :
is derived from the normal distibution. Used in situations, such as
asset returns where the value cannot be negative.
- Normal :
The normal distribution is the standard probability distribution known as the Guassian, or the bell curve.
It is one or the most common distributions used in statistical modeling, usually because of its use in the
central limit theorem.
- Poisson :
The poisson distribution measures the probability of a number of events ocurring. As such,
it is a probability over a discrete non-negative variable.
- T Distribution :
- Uniform :
a variable that can take any of a continuum of values with equal likelihood.
- Weibull :
Additional Topics
- Joint Distributions
- describes distributions over multiple random variables.
- Density Estimation refers to the set
of tools that have been developed to estimate an unknown density from a series of observations.
- Exponential Familty
of distributions refers to a set of distributions that can all be put in set form. Distributions in the
exponential family oftern share a number a algorithms that can apply to any member of the family.
- Distance Measures
are functions that compare two distributions and return a number that represents how similar or disimilar the distributions
are.
- Plotting a Distribution
