Description

This calculator gives the value of the cumulative distribution function \(q = F(x)\) for a given value of \(x\), or the value of the quantile function \(x = F^{-1}(q)\) for a given value of \(q\). Each of the following special distribution can be selected with the list box:

• The (continuous) arcsine distribution on the interval \( (0, b) \).
• The (discrete) arcsine distribution on \( \{0, 1, \ldots, n\} \)
• The Benford's first digit distribution with base \( b \)
• The Benford mantissa distribution with base \( b \)
• The beta distribution with left shape parameter \(a\) and right shape parameter \(b\)
• The beta-binomial distribution with left beta parameter \( a \), right beta parameter \( b \), and \( n \) trials
• The beta-negative binomial distribution with left beta parameter \( a \), right beta parameter \( b \), and \( k \) successes
• The beta prime distribution with shape parameters \( a \) and \( b \)
• The binomial distribution with parameters \( n \) and \( p \)
• The birthday distribtuion with population size \( m \) and sample size \( n \)
• The Cauchy distribution with location parameter \( a \) and scale parameter \( b \)
• The chi-square distributon with \(n\) degrees of freedom
• The coupon collector distribution with population size \( m \) and distinct size \( k \)
• The exponential distribution with scale parameter \(b\)
• The exponential-logarithmic distribution with shape parameter \( p \) and scale parameter \( b \)
• The extreme value distribution
• The finite order statistic distribution with population size \( m \), sample size \( n \), and order \( k \)
• The Fisher \(F\) distribution with \(n\) degrees of freedom in the numerator and \(d\) degrees of freedom in the denominator
• The folded-normal distribution with parameters \( \mu \) and \( \sigma \)
• The gamma distribution with shape parameter \(k\) and scale parameter \(b\)
• The geometric distribution with success parameter \(p\)
• The hypergeometric distribution with parameters \( m \), \( r \), and \( n \)
• The hyperbolic secant distribution with location parameter \( \mu \) and scale parameter \( \sigma \)
• The Irwin-Hall distribution with \( n \) terms
• The Laplace (double exponential) distribution with location parameter \( a \) and scale parameter \( b \)
• The logarithmic series distribution with shape parameter \( p \)
• The logistic distribution with location parameter \(a\) and scale parameter \(b\)
• The log-logistic distribution with scale parameter \( a \) and shape parameter \( b \)
• The lognormal distribution with parameters \(\mu\) and \(\sigma\)
• The matching distribution with parameter \( n \)
• The Maxwell-Boltzmann distribution with shape parameter \( a \)
• The Pareto distribution with shape parameter \(k\) and scale parameter \(b\)
• The Poisson distribution with parameter \( \lambda \)
• The Pólya distribution with parameters \( a \), \( b \), \( c \), and \( n \)
• The negative binomial distribution with parameters \( k \) and \( p \)
• The normal distribuiton with mean \(\mu\) and standard deviation \(\sigma\)
• The semicircle distribution with center \(a\) and radius \( r \)
• The student \(t\) distribution with \(n\) degrees of freedom
• The triangle distribution with location parameter \( a \), scale parameter \(w \) and shape parameter \(p\).
• The (continuous) uniform distribution on the interval \( [a, a + w] \)
• The (discrete) uniform distribution on \( \{a, a + 1, \ldots, a + n\} \)
• The U-Quadratic distribution on the interval \( [a, a + w] \)
• The Weibull distribution with shape parameter \(k\) and scale parameter \(b\)
• The zeta distribution with shape parameter \( a \)

The parameters of the distribution, and the variables \(x\) and \(q\) can be varied with the input controls.