quantile function

In other cases the quantile functions may be developed as power series.

More generally, one can consider the quantile function for any distribution.

The inverse of the cdf is called the quantile function.

It is the reciprocal of the pdf composed with the quantile function.

One then uses the quantile function with these estimated parameters to give a prediction interval.

The n-th order central moment can be expressed in terms of the quantile function:

Statistical applications of quantile functions are discussed extensively by Gilchrist.

In such a case, this defines the inverse distribution function or quantile function.

That is, a probability plot can easily be generated for any distribution for which one has the quantile function.

Another, more robust graphical method uses bundles of residual quantile functions.

Quantile regression is desired if conditional quantile functions are of interest.

Quantile functions are used in both statistical applications and Monte Carlo methods.

Other algorithms to evaluate quantile functions are given in the Numerical Recipes series of books.

Suppose the th conditional quantile function is .

Quantile functions may also be characterized as solutions of non-linear ordinary and partial differential equations.

In other words if you have a record of portfolio value over time then the VaR is simply the negative quantile function of those values.

The quantile function (inverse cumulative distribution function) is :

These can be expressed in terms of the quantile function and the order statistic medians for the continuous uniform distribution by:

Quantile function, for the explicit construction of inverse CDFs.

In addition, R offers a cumulative distribution function () and a quantile function () for q.

Inverse CDFs are also called quantile functions.

The quantile function is the inverse of the cumulative distribution function (probability that X is less than or equal to some value).

The non-linear ordinary differential equation given for normal distribution is a special case of that available for any quantile function whose second derivative exists.

The quantile function can be expressed in a closed-form expressions using the Lambert W function:

Inverse distribution function (quantile function)