Distribution Navigator

From countless probability distributions, you're sure to find one that perfectly fits your purpose!

(To find the optimal distribution based on data characteristics ⇒Gallery of Distributions)

For cases dealing with integers such as counts or number of people

Data Range	Distribution Name	Description
Finite	Bernoulli	Success or failure. An all-or-nothing model. Coin toss is a typical example.
	Uniform(discrete)	Distribution of "equally likely" outcomes. Dice, Roulette Random sampling Shuffling (Random shuffle) Fair coin. Toss a coin and take 1 step right if heads, 1 step left if tails... This is a one-dimensional random walk. Four-sided fair die. Each face is labeled "Right", "Left", "Forward", "Backward". Roll the die and take 1 step in the direction shown... This is a two-dimensional random walk. Six-sided fair die. Each face is labeled "Right", "Left", "Forward", "Backward", "Up", "Down". Roll the die and take 1 step in the direction shown... This is a three-dimensional random walk.
Infinite	Poisson	Distribution of events that occur randomly and infrequently. Number of emails per hour Number of airplane accidents per year Number of restaurants per km of national highway The "infrequently" part is important. For high-frequency events, it can be approximated by a Normal(Single)

For cases dealing with any values, not limited to integers, such as weight, length, time, rate of return...

Data Range	Distribution Name	Description
Finite	Beta	Has a high degree of freedom in shape, so it can fit various distributions. Good to try for finite interval data with unclear characteristics that don't fit well with normal distribution.
	Johnson SB	Like the Beta, it can be used to fit data of unknown nature in a finite interval with asymmetric shape. Mean, standard deviation, skewness, and kurtosis can be freely adjusted. Used in forestry (distribution of tree trunk diameters in forests).
	Kumaraswamy	When Beta distribution and Johnson SB distribution are too complex, but triangular distribution is too simple... This might be just right.
	Triangular	Easy to handle due to its simple distribution function. Can be used instead of Beta or Johnson SB for finite interval distributions with a single peak and left-right asymmetry.
	Uniform	The base random number used in the inverse function method to generate random numbers following other distributions.
	U Quadratic	The simplest U-shaped distribution. Can be an alternative to Beta distribution.
Semi-Infinite	Exponential	Distribution of "intervals" between rare events. Intervals between accidents Intervals between customer arrivals at a convenience store Intervals between radioactive decay events If events occur following this distribution, their frequency follows a Poisson .
	Gumbel Type II	Extreme value theory
	Log Normal	Distribution of annual income Distribution of logarithmic returns on stock prices The logarithm of these data follows a normal distribution. In this case, the original data follows a log-normal distribution.
	Pareto	Originally developed as a model for income distribution. One of the distributions known as power-law distributions. It's becoming increasingly important as various phenomena are found to follow power-law distributions. Distribution of savings amounts Shape of distribution tails (extreme value theory)
	Weibull	A representative distribution for failure rates in reliability engineering. Also used in extreme value theory.
	Chi	Can someone explain?
	Chi square	Chi-square test
	Gamma	Precipitation amount distribution. Insurance claim amount distribution.
	F	F test
Infinite	Cauchy	Like the normal distribution, it's a distribution with a single peak over an infinite interval. However, it's used as a distribution with far more outliers than can be explained by a normal distribution.
	Gumbel Type I	Extreme value theory
	Johnson SU	It has heavier tails than the normal distribution and allows for adjustment of skewness and kurtosis. It's gaining attention as a replacement for the normal distribution in VaR calculations, etc.
	Laplace	Can someone explain?
	Logistic	Similar to the normal distribution but with slightly heavier tails. It's sometimes used instead of the normal distribution because its equation is simpler and easier to handle. Also, its Cumulative Distribution Function is called the "logistic curve" and is applied in various fields. Spread of infectious diseases Sales pattern of new products Population growth model Proficiency level
	Normal(Single)	A fundamental distribution that appears everywhere. You can't do anything without knowing this.
	Normal(Multi)	Used for calculating VaR of portfolios through Monte Carlo simulation.
	t	t test