Statistical Distributions by Nick T. Thomopoulos

Author:Nick T. Thomopoulos
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

© Springer International Publishing AG 2017

Nick T. ThomopoulosStatistical Distributionshttps://doi.org/10.1007/978-3-319-65112-5_10

10. Left Truncated Normal

Nick T. Thomopoulos1

(1)Stuart School of Business, Illinois Institute of Technology, Burr Ridge, IL, USA

10.1 Introduction

In an earlier book [Thomopoulos (1980) p 318–324], the author shows how to use the left-truncated normal distribution to applications in inventory control.

The left-truncated normal (LTN) has many shapes that range from normal to exponential-like. The distribution has one parameter k that is a particular value of the standard normal z, and the distribution includes all values of z larger than k. The variable is denoted as t where t = (z – k), and since z is equal or larger than k, t is zero or larger. The key measures of the distribution are the mean, standard deviation, coefficient-of-variation, and a new measure called the spread ratio. The spread ratio is always larger than zero. Another measure is tα = α-percent –point of t that gives the value of t with cumulative probability α. Of immediate interest is t0.01 and t0.99. All of these measures are listed in a table for each k ranging from −3.0 to +3.0. When an analyst has sample data (x1, …, xn) and draws certain stats from the data including an estimate of the spread-ratio, the analyst can identify if any of the LTN distributions are a better fit to the data than the normal distribution. If any is selected, the low-limit, denoted as γ, where x ≥ γ is caluculated. The chapter also shows how to compute xα = α-percent-point of x for any α.

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