Point Estimate Calculator

Calculate population parameter estimates using MLE, Wilson, Laplace, and Jeffrey methods

Calculate Point Estimates

Number of Successes (S)

Number of favorable outcomes (e.g., heads in coin tosses)

Number of Trials (T)

Total number of trials or attempts

Confidence Level (%)

Probability that the estimate is correct within margin of error (Z-score: 1.960)

Point Estimation Results

Best Point Estimate

91.1765%

Method: Laplace

MLE ≥ 0.9: Laplace estimation is smaller and more conservative for high probabilities

92.00%

MLE

S/T

90.45%

Wilson

(S+z²/2)/(T+z²)

91.18%

Laplace

(S+1)/(T+2)

91.58%

Jeffrey

(S+0.5)/(T+1)

Detailed Calculations

MLE: 92 ÷ 100 = 0.920000

Laplace: (92 + 1) ÷ (100 + 2) = 0.911765

Jeffrey: (92 + 0.5) ÷ (100 + 1) = 0.915842

Wilson: (92 + 1.960²/2) ÷ (100 + 1.960²) = 0.904463

Step-by-Step Example

Biased Coin Problem

Problem: You toss a coin 100 times and get 92 heads. What's the probability of heads?

Given: S = 92 successes, T = 100 trials, Confidence = 95%

Z-score: 1.960 (for 95% confidence level)

Solution Steps

1. MLE = 92/100 = 0.92

2. Laplace = (92+1)/(100+2) = 93/102 = 0.9118

3. Jeffrey = (92+0.5)/(100+1) = 92.5/101 = 0.9158

4. Wilson = (92+1.96²/2)/(100+1.96²) = 0.9089

5. Since MLE ≥ 0.9, choose smaller of Jeffrey/Laplace = 0.9118 (91.18%)

Best Method Selection

MLE ≤ 0.5

Use Wilson Estimation

Best for low probabilities

0.5 < MLE < 0.9

Use Maximum Likelihood

Most accurate in this range

MLE ≥ 0.9

Use smaller of Jeffrey/Laplace

Conservative for high probabilities

Point Estimate Formulas

Maximum Likelihood (MLE)

MLE = S / T

Laplace Estimation

Laplace = (S + 1) / (T + 2)

Jeffrey Estimation

Jeffrey = (S + 0.5) / (T + 1)

Wilson Estimation

Wilson = (S + z²/2) / (T + z²)

Quick Tips

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Point estimates give single "best guess" values

•

Different methods work better in different ranges

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Larger sample sizes generally give more accurate estimates

•

Consider confidence intervals for range estimates

Understanding Point Estimation

What is Point Estimation?

Point estimation is a statistical method used to estimate unknown population parameters using sample data. Unlike interval estimation, which provides a range of values, point estimation gives a single "best guess" value for the parameter of interest.

Common Applications

•Estimating success rates in clinical trials
•Quality control in manufacturing
•Market research and polling
•Reliability testing

Why Multiple Methods?

Different estimation methods have varying strengths depending on the data characteristics. The calculator automatically selects the most appropriate method based on statistical principles and the value of the Maximum Likelihood Estimate.

Method Characteristics

MLE:Unbiased, most accurate for moderate probabilities
Wilson:Better performance near boundaries (0 or 1)
Laplace:Conservative, adds uniform prior
Jeffrey:Non-informative Bayesian approach

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