See: Description
| Interface | Description |
|---|---|
| ProbabilityDistribution |
A univariate probability distribution completely characterizes a random variable by stipulating
the probability of each value of a random variable (when the variable is discrete), or the
probability of the value falling within a particular interval (when the variable is continuous).
\[
F(x) = Pr(X < x)
\]
Selecting an operation
Use
ProbabilityDistribution.cdf(double) to compute a cumulative probability and
ProbabilityDistribution.quantile(double) to invert it. |
| Class | Description |
|---|---|
| BetaDistribution |
The beta distribution is the posterior distribution of the parameter p of a binomial
distribution
after observing α - 1 independent events with probability p and
β - 1 with probability 1 - p,
if the prior distribution of p is uniform.
|
| BinomialDistribution |
The binomial distribution is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments,
each of which yields success with probability p.
|
| ChiSquareDistribution |
The Chi-square distribution is the distribution of
the sum of the squares of a set of statistically independent standard Gaussian random variables.
|
| EmpiricalDistribution |
An empirical cumulative probability distribution function
is a cumulative probability distribution function that
assigns probability 1/n at each of the n numbers in a sample.
|
| ExponentialDistribution |
The exponential distribution describes the times between events in a Poisson process,
a process in which events occur continuously and independently at a constant average rate.
|
| FDistribution |
The F distribution is the distribution of the ratio of two independent chi-squared variates.
|
| GammaDistribution |
This gamma distribution, when k is an integer, is the distribution of
the sum of k independent exponentially distributed random variables,
each of which has a mean of θ (which is equivalent to a rate parameter of
\(\theta ^{-1}\)).
|
| LogNormalDistribution |
A log-normal distribution is a probability distribution of a random variable whose logarithm is normally distributed.
|
| NormalDistribution |
The Normal distribution has its density a Gaussian function.
|
| PoissonDistribution |
The Poisson distribution (or Poisson law of small numbers) is a discrete probability distribution
that expresses the probability of a given number of events occurring in a fixed interval of time
and/or space if these events occur with a known average rate and independently of the time since
the last event.
|
| RayleighDistribution |
The L2 norm of (x1, x2), where \(x_{i}\)'s are normal, uncorrelated, equal variance and
have the Rayleigh distributions.
|
| TDistribution |
The Student t distribution is the probability distribution of t, where
\[
t = \frac{\bar{x} - \mu}{s / \sqrt N}
\]
\(\bar{x}\) is the sample mean;
μ is the population mean;
s is the square root of the sample variance;
N is the sample size;
The importance of the Student's distribution is
when (as in nearly all practical statistical work) the population standard deviation is unknown and has to be estimated from the data.
|
| TriangularDistribution |
The triangular distribution is a continuous probability distribution with lower limit a, upper
limit b and mode c, where a < b and a ≤ c ≤ b.
|
| TruncatedNormalDistribution |
The truncated Normal distribution is the probability distribution of a normally distributed
random variable whose value is either bounded below or above (or both).
|
| WeibullDistribution |
The Weibull distribution interpolates between the exponential distribution k = 1 and the
Rayleigh distribution (k = 2),
where k is the shape parameter.
|
NormalDistribution shows how to
compute a cumulative probability and an inverse quantile.
ProbabilityDistribution describes
the common interface. Check each concrete distribution's parameter units,
support, and accepted probability endpoints.
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