Point Estimate Calculator

A point estimate is like a best guess of a population parameter.

Enter the number of successes, sample size and confidence level in the calculator below and then click on the "Calculate" button to compute the point estimate based on the four estimation methods - Maximum Likelihood Estimate (MLE), Wilson Estimate, Laplace Estimate and Jeffrey Estimate.

Number of Successes (x) Sample Size (n) Confidence Level (α)

Z score (z) = 1.96

Results

Estimation Techniques

The formulas for various estimation techniques used to calculate the point estimate are as follows:

Maximum Likelihood Point Estimate (MLE): x / n
Wilson Point Estimate: (x + z²/2) / (n + z²)
Jeffrey Point Estimate: (x + 0.5) / (n + 1)
Laplace Point Estimate: (x + 1) / (n + 2)

where x is the number of successes in the sample, n is the sample size or number of trials and z is the z-score as per the confidence level.

The calculator above is based on the following logic to find out the best point estimate :

If x/n ≤ 0.5, the Wilson Point Estimate is used.
If 0.5 < x/n < 0.9, the Maximum Likelihood Point Estimate is used.
If 0.9 ≤ x/n < 1.0, take the smallest of the Jeffrey and Laplace Estimation methods.
If x/n = 1.0, the Laplace Point Estimate is used.