How to Find Maximum of Normal Distribution Using Kolmogorov Smirnov Test - Tutorial

Definition:

Kolmogorov Smirnov test (K-S test) is a statistical analysis, used to evaluate probability of normal distribution for mean variables.

Formula:

Where, D = Maximum Value of Normal Distribution, N = Number of Statistic Data, F = Kolmogorov-Smirnov Index.

Example:

Calculate maximum of normal distribution mean variable for 6 rows from date set of population {120,123,110,100,200,210} using Kolmogorov Smirnov test method.

Given:

Solution:

Substitute the given values in the formula to solve maximum of normal distribution,

Step1:

First, calculate the value of Mean(μ)

Step2:

Standard Deviation (σ) = √∑(X-μ)² / n-1 = √∑(120-143.8)² + (123-143.8)² + (110-143.8)² + (100-143.8)² + (200-143.8)² + (210-143.8)² / 5 = √2320.166 = 48.168

Step3:

F₀(100) = P_{μ=143.833, σ=14.85} (100) P_{μ=143.833, σ=14.85} (100) = Normal[(100 - 143.833) / 48.168] = 0.181409 F_n(100) = 1/n = 1/6 = 0.167 F_n-1(100) = (i-1)/n = (1-1)/6 = 0

Step4:

Follow the procedure of Step 3, upto N th value.

Step5:

The following table shows all the values