# Limiting forms of the frequency distribution of the largest or smallest member of a sample

```@article{FisherLimitingFO,
title={Limiting forms of the frequency distribution of the largest or smallest member of a sample},
author={R. A. Fisher and Leonard Henry Caleb Tippett},
journal={Mathematical Proceedings of the Cambridge Philosophical Society},
volume={24},
pages={180 - 190}
}```
• Published 1 April 1928
• Mathematics, Geology
• Mathematical Proceedings of the Cambridge Philosophical Society
Summary The limiting distribution, when n is large, of the greatest or least of a sample of n, must satisfy a functional equation which limits its form to one of two main types. Of these one has, apart from size and position, a single parameter h, while the other is the limit to which it tends when h tends to zero. The appropriate limiting distribution in any case may be found from the manner in which the probability of exceeding any value x tends to zero as x is increased. For the normal…
2,961 Citations

### The asymptotical distribution of range in samples from a normal population.

1. Introductory. Consider a sample of n observations, taken from an infinite normal population with the mean 0 and the standard deviation 1. Let a be the smallest and b the greatest of the observed

### Linear estimates with polynomial coefficients.

No attempt has been made to obtain estimates which in any sense approximate to the best (least-squares) estimates, but two examples (the normal distribution and the extreme value distribution) are used to illustrate the method.

### DISTRIBUTION OF THE MAXIMUM OF THE ARITHMETIC MEAN OF CORRELATED RANDOM VARIABLES

1. Summary. The initial distribution considered here is obtained from a multivariate analogue of the Pearson Type III distribution, and the value of the correlation is taken to be non-negative. There

### Extreme Value Theory

We describe the limiting behaviour of extreme values generated by a finite sequence (or time-series) of random variables when the number of observations becomes increasingly large. Under the

### APPROXIMATE FORMULAE FOR THE STATISTICAL DISTRIBUTIONS OF EXTREME VALUES

0 1. SUMMARY This paper deals with the distribution function of the order statistics xn_m+l(m = 1, 2 ... ), Mn,m(x). For this distribution function of the mth largest value (if m is counted from

### Accurately approximating extreme value statistics

• Mathematics
Journal of Physics A: Mathematical and Theoretical
• 2021
We consider the extreme value statistics of N independent and identically distributed random variables, which is a classic problem in probability theory. When N → ∞, fluctuations around the maximum

### Large deviations of the maximum of independent and identically distributed random variables

A pedagogical account of some aspects of extreme value statistics (EVS) is presented from the somewhat non-standard viewpoint of large deviation theory. We address the following problem: given a set

### Maximum-Likelihood Estimation, from Doubly Censored Samples, of the Parameters of the First Asymptotic Distribution of Extreme Values

• Mathematics
• 1968
Let X be a random variable having the first asymptotic distribution of smallest (largest) values, with location parameter u and scale parameter b, b > 0. The natural logarithm of the likelihood

### The rate of convergence of extremes of stationary normal sequences

• H. Rootzén
• Mathematics
Advances in Applied Probability
• 1983
Let {ξ; t = 1, 2, …} be a stationary normal sequence with zero means, unit variances, and covariances let be independent and standard normal, and write . In this paper we find bounds on which are

### Estimates of extreme values by different distribution functions

• Mathematics
• 1965
A comparative study of the estimates of extreme values as would be given by log-normal distribution, extreme-value distribution, and Foster's type 3 distribution has been made under the assumption