In probability and statistics, the quantile function is a function Q : [ 0 , 1 ] ↦ R {\displaystyle Q:[0,1]\mapsto \mathbb {R} } which maps some probability...

distribution function of a random variable is known, the q-quantiles are the application of the quantile function (the inverse function of the cumulative...

{\pi /2}}}}} . The quantile function of a distribution is the inverse of the cumulative distribution function. The quantile function of the standard normal...

regression goes beyond this and is advantageous when conditional quantile functions are of interest. Different measures of central tendency and statistical...

plot (quantile–quantile plot) is a probability plot, a graphical method for comparing two probability distributions by plotting their quantiles against...

distribution function (quantile function) of the logistic distribution is a generalization of the logit function. Its derivative is called the quantile density...

In statistics, the logit (/ˈloʊdʒɪt/ LOH-jit) function is the quantile function associated with the standard logistic distribution. It has many uses in...

{\displaystyle F(x)=p} . This defines the inverse distribution function or quantile function. Some distributions do not have a unique inverse (for example...

simulation studies since its probability density function, cumulative distribution function and quantile functions can be expressed in closed form. This distribution...

of fitting to data with linear least squares; simple, closed-form quantile function (inverse CDF) equations that facilitate simulation; a simple, closed-form...

In statistics, quartiles are a type of quantiles which divide the number of data points into four parts, or quarters, of more-or-less equal size. The...

In probability theory and statistics, the probit function is the quantile function associated with the standard normal distribution. It has applications...

and statistics, a probability mass function (sometimes called probability function or frequency function) is a function that gives the probability that a...

involves computing the quantile function of the distribution — in other words, computing the cumulative distribution function (CDF) of the distribution...

/2;k+1,1),} where χ 2 ( p ; n ) {\displaystyle \chi ^{2}(p;n)} is the quantile function (corresponding to a lower tail area p) of the chi-squared distribution...

distribution that has a constant failure rate. The quantile function (inverse cumulative distribution function) for Exp(λ) is F − 1 ( p ; λ ) = − ln ⁡ ( 1 −...

}}\arctan \left({\frac {x-x_{0}}{\gamma }}\right)+{\frac {1}{2}}} and the quantile function (inverse cdf) of the Cauchy distribution is Q ( p ; x 0 , γ ) = x...

continuous, symmetric probability distribution defined in terms of its quantile function. It is typically used to identify an appropriate distribution (see...

called the quantile function, and the integrals are of the Riemann–Stieltjes kind. If a random variable X has a probability density function then the characteristic...

Φ is known as the normal quantile function, or probit function and may be expressed in terms of the inverse error function as probit ⁡ ( p ) = Φ − 1...

A quantile-parameterized distribution (QPD) is a probability distributions that is directly parameterized by data. They were created to meet the need for...

a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given...

Φ is the cumulative distribution function of the standard normal distribution. The formula for the quantile function is G ( p ) = 1 4 [ γ Φ − 1 ( p )...

instance of the hypergeometric function. For information on its inverse cumulative distribution function, see quantile function § Student's t-distribution...

mathematics, the moments of a function are certain quantitative measures related to the shape of the function's graph. If the function represents mass density...

defined using the cumulant-generating function K(t), which is the natural logarithm of the moment-generating function: K ( t ) = log ⁡ E ⁡ [ e t X ] . {\displaystyle...

variable, a location at which the probability density function has a local peak. Quantile: the q-quantile is the value x {\displaystyle x} such that P ( X...

us.mensa.org. Retrieved 22 February 2023. See Normal distribution#Quantile function. American Mensa. "Take the Mensa Admission Test". www.us.mensa.org...

In probability theory and statistics, the moment-generating function of a real-valued random variable is an alternative specification of its probability...

computed in exactly the same way. The normal quantile function Φ−1 is simply replaced by the quantile function of the desired distribution. In this way,...