# Package com.numericalmethod.suanshu.stats.distribution.univariate

• Interface Summary
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).
• Class Summary
Class Description
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.
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 xi'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.