page_title: List of probability distributions
section_title: Supported on a bounded interval
hierarchical_section_title: List of probability distributions / Continuous distributions / Supported on a bounded interval
context_page_description: Many probability distributions that are important in theory or applications have been given specific names.
context_section_description: The arcsine distribution on [a,b], which is a special case of the Beta distribution if α=β=1/2, a=0, and b = 1.
  The Beta distribution on  [0,1], a family of two-parameter distributions with one mode, of which the uniform distribution is a special case, and which is useful in estimating success probabilities.
  The logit-normal distribution on (0,1).
  The Dirac delta function although not strictly a distribution, is a limiting form of many continuous probability functions.  It represents a discrete probability distribution concentrated at 0 — a degenerate distribution — but the notation treats it as if it were a continuous distribution.
  The uniform distribution or rectangular distribution on [a,b], where all points in a finite interval are equally likely.
  The Irwin–Hall distribution is the distribution of the sum of n independent random variables, each of which having the uniform distribution on [0,1].
  The Bates distribution is the distribution of the mean of n independent random variables, each of which having the uniform distribution on [0,1].
  The Kent distribution on the two-dimensional sphere.
  The Kumaraswamy distribution is as versatile as the Beta distribution but has simple closed forms for both the cdf and the pdf.
  The Marchenko–Pastur distribution is important in the theory of random matrices.
  The PERT distribution is a special case of the beta distribution
  The raised cosine distribution on []
  The reciprocal distribution
  The triangular distribution on [a, b], a special case of which is the distribution of the sum of two independent uniformly distributed random variables (the convolution of two uniform distributions).
  The trapezoidal distribution
  The truncated normal distribution on [a, b].
  The U-quadratic distribution on [a, b].
  The von Mises–Fisher distribution on the N-dimensional sphere has the von Mises distribution as a special case.
  The Wigner semicircle distribution is important in the theory of random matrices.
  The continuous Bernoulli distribution is a one-parameter exponential family that provides a probabilistic counterpart to the binary cross entropy loss.
caption: Chi-squared distribution
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