A Distribution of the First Order Statistic When the Sample Size is Random

• Main Author: Forgo, Vincent Z, Mr
• Format: Others
• Language: English
• Published: Digital Commons @ East Tennessee State University 2017
• Subjects: Minimum order statistics or first order statistics; Cumulative density function; Probability density function; Expectation; Variance; Percentile; Statistical Theory
• Online Access: https://dc.etsu.edu/etd/3181; https://dc.etsu.edu/cgi/viewcontent.cgi?article=4586&context=etd

Statistical distributions also known as probability distributions are used to model a random experiment. Probability distributions consist of probability density functions (pdf) and cumulative density functions (cdf). Probability distributions are widely used in the area of engineering, actuarial science, computer science, biological science, physics, and other applicable areas of study. Statistics are used to draw conclusions about the population through probability models. Sample statistics such as the minimum, first quartile, median, third quartile, and maximum, referred to as the five-number summary, are examples of order statistics. The minimum and maximum observations are important in extreme value theory. This paper will focus on the probability distribution of the minimum observation, also known as the first order statistic, when the sample size is random.