**Normal distribution. **Standard error of quantile estimate is:

where *z*_{p} is standard normal variable corresponding to probability of nonexceedance *p*, *s*_{x} is standard deviation of normal variable *X*, i.e. of sample data, and *n* is sample size.

**Log-normal distribution. **For a log-normally distributed variable *X*, variable *Y* = ln *X* (or *Y* = log *X*) is normally distributed. From results for normal distribution, standard error of a normal quantile estimate *y*_{p} is:

where *s*_{y} is standard deviation of logarithms of sample data. Confidence limits for *y*_{p} are then:

From the above, approximate confidence limits for the original variable *X* = *e*^{Y} are:

Alternatively, if base 10 logarithms were used, then the approximate confidence limits for the original variable *X* = *10*^{Y} are:

**Pearson type 3 distribution****. **Approximate standard error for the Pearson 3 quantile is can be calculated using the following rather cumbersome expression:

where *s*_{x} is standard deviation of *X*, *n* is sample size, and d is calculated as square root from:

where *K*_{p} is frequency factor the Pearson 3 distribution, which depends only on coefficient of skewness *C*_{s}, and *K'*_{p} is its derivative. Frequency factor can be read from statistical tables, while the following analytical approximation is often used:

where *z*_{p} is standard normal variable corresponding to the nonexceedance probability *p*. Derivative of *K*_{p} can be found from the above expression and it is equal to:

**Log-Pearson type 3 distribution****. **Similar to log-normal distribution, the easiest way to construct confidence interval for log-Pearson 3 distribution is to find confidence limits for the transformed variable *Y* = ln *X* (or *Y* = log *X*) and to use standard error for Pearson 3 distribution with standard deviation and coefficient of skewness of logarithms (*s*_{y} and *C*_{sy}). An inverse transformation is then needed to obtain confidence limits for the original variable *X*.

**Gumbel (EV1) distribution****. **For the Gumbel distribution with parameters estimated by the method moments, standard error of the *p*-quantile is:

where *K*_{p} is frequency factor for the Gumbel distribution, *s*_{x} is standard deviation of *X*, and *n* is sample size. Gumbel frequency factor depends only on nonexceedance probability since it can be expressed using Gumbel standard variable *y*_{p}: