Class Summary |
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
θ^{-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. |
WeibullDistribution |
The Weibull distribution interpolates between the exponential distribution k = 1 and the Rayleigh distribution (k = 2),
where k is the shape parameter. |