Using the sample maximum to estimate the parameters of the underlying distribution

We propose novel estimators for the parameters of an exponential distribution and a normal distribution when the only known information is a sample of sample maxima; i.e., the known information consists of a sample of m values, each of which is the maximum of a sample of n independent random variabl...

Full description

Saved in:
Bibliographic Details
Published in:PloS one 2019-04, Vol.14 (4), p.e0215529-e0215529
Main Authors: Capaldi, Alex, Kolba, Tiffany N
Format: Article
Language:English
Subjects:
Analysis
Arabidopsis
Arabidopsis - anatomy & histology
Arabidopsis thaliana
Computer simulation
Data Interpretation, Statistical
Estimators
Expected values
Extreme value theory
Extreme values
Flowering
Independent variables
Laboratories
Maxima
Maximum likelihood (Statistics)
Methods
Models, Statistical
Normal Distribution
Novels
Organ Size
Parameter estimation
Pollen
Pollen Tube - anatomy & histology
Pollen tubes
Probability distribution functions
Random variables
Sample Size
Sampling distributions
Skewness
Theory
Tubes
Variance
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We propose novel estimators for the parameters of an exponential distribution and a normal distribution when the only known information is a sample of sample maxima; i.e., the known information consists of a sample of m values, each of which is the maximum of a sample of n independent random variables drawn from the underlying exponential or normal distribution. We analyze the accuracy and precision of the estimators using extreme value theory, as well as through simulations of the sampling distributions. For the exponential distribution, the estimator of the mean is unbiased and its variance decreases as either m or n increases. Likewise, for the normal distribution, we show that the estimator of the mean has negligible bias and the estimator of the variance is unbiased. While the variance of the estimators for the normal distribution decreases as m, the number of sample maxima, increases, the variance increases as n, the sample size over which the maximum is computed, increases. We apply our method to estimate the mean length of pollen tubes in the flowering plant Arabidopsis thaliana, where the known biological information fits our context of a sample of sample maxima.
ISSN:1932-6203
1932-6203
DOI:10.1371/journal.pone.0215529