Presenting One Probability Distribution as a Function of Another — Some Applications

SYNOPTIC ABSTRACT

Imagine two probability density functions for a continuous variate, which differ in their means, but have similar standard deviations. There is a threshold at some value of the variate. As this threshold reduces in value, the probability of the variate exceeding the threshold increases, for both probability density functions. The graph obtained by plotting the two probabilities of threshold exceedance as a function of each other is the theme of this paper. Among the better-known applications of such a graph are signal detection theory (psychology), the multifactorial model of disease transmission (genetics), Lorenz curves (economics), and Bradford's law (information Science).

Key Words and Phrases:

• graphical presentation
• Lorenz curve
• pairchart
• signal detection theory