Hi all. Recently, while skimming through a book on ROC curves, I came across this term "monotone distribution." I tried googling it but didn't find any satisfactory answer. Can someone please explain what a monotone distribution is, in simple terms. I am a non-mathematician and just want a feel of it.
Thank you.
Inaamul Haq A monotonic distribution is a function in which the curve never reverses direction. For example, a curve that increases along the x-axis, but never decreases (or a curve that decreases along the x-axis, but never increases). See the images below
Thank you Blaine Tomkins .
A normal distribution is a non-monotonic distribution? Is that right?
Monotone Distribution Defined
Monotone distribution
A monotonic distribution is a statistical distribution in which the values either always increase or always decrease as the values of the independent variable increase. In other words, the distribution has either a positive or negative association between the independent and dependent variables.
A monotone distribution can be either increasing or decreasing, but it cannot change direction. For example, if the distribution is increasing, the values of the dependent variable will always increase as the independent variable increases, and vice versa.
In probability theory, monotonicity is an important property because it can simplify the calculation of probabilities and other statistical measures. For example, if a distribution is monotonically increasing, its cumulative distribution function (CDF) will be a non-decreasing function, which makes it easier to calculate probabilities and percentiles.
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