Point Estimate Calculator

An online point estimate calculator helps you to find the best approximate value of the unknown population parameter with different approximation techniques. This point estimator provides z score values, Laplace, Jeffrey, Wilson, and Maximum Likelihood Estimation (MLE). In the following text, you can learn how to find point estimate with a confidence interval, the number of successes and trials.

What is a Point Estimate in Stats?

In statistics, point estimation involves using sample data to evaluate a single value (called point estimation because it defines a point in specific parameter space) to be used as the best estimate or guess of the unknown population parameters.

Point Estimate Formulas:

You can use four different point formulas: MLE (Maximum Likelihood Estimation), Wilson, Laplace, and Jeffrey estimation. Each method produces slightly different results and should be used in different situations.

To calculate estimate points, you need the following value:

• Number of trails T
• Number of successes S
• Confidence interval
• Z score z

Once these values ​​are known, the point estimate can be calculated according to the following formula:

• Maximum Likelihood Estimation = Number of successes (S) / Number of trails (T)
• Laplace Estimation = (Number of successes (S) + 1) / (Number of trails (T) + 2)
• Jeffrey Estimation = (Number of successes (S) + 0.5) / (Number of trails (T) + 1)
• Wilson Estimation = (Number of successes (S) + \( z^2/2 \)) / (Number of trails (T) + \( z^2 \) )

After calculating all four values, the point estimate calculator chooses the most accurate one. This must be done according to the following rules:

• If MLE is less than 0.5, then Wilson’s estimate is the most accurate.
• If 0.5 <MLE <0.9, then the MLE is the most accurate.
• If it is 0.9 <MLE, then the lowest estimate of Jeffrey and Laplace is the most accurate.

However, an Online Laplace Transform Calculator will help you to provide the transformation of the real variable function to the complex variable.

How to Calculate Point Estimate?

The following example is a stepwise process for calculating point estimates.

• First, we need to determine the missing variables to calculate point estimates. In this case, the variable is S, the number of successes, T-the number of trails, and the z-confidence interval.
• The next step is to determine the values ​​for all these variables.
• Lastly, substitute all the data into the formula.

Example:

If any coin is tossed 4 times out of nine trials with a confidence interval level of 95%, then tell the best point of success of that coin?

Solution:

Given Values:

Number of successes = 4

Number of Trials = 9

Confidence Interval Level = 95% = 0.95.

In order to calculate the best point estimation, let evaluate all values:

MLE = S / T

= 4 / 9

= 0.4444

Laplace = S + 1 / T + 2

= 4 + 1 / 9 + 2

= 5 / 11

= 0.4545

Jeffrey = S + 0.5 / T + 1

= 4 + 0.5 / 9 + 1

= 4.5 / 10

= 0.45

Z-Critical Value (z) = for 95% level = – 1.96

Wilson = S + (Z^2 / 2) / T + z^2

= 4 + ((-1.96)^2 / 2) / 9 + (-1.96)^2

= 0.4611

Hence, the 0.4611 is the Best Point Estimation as MLE ≤ 0.5

General Methods of Finding the Point Estimate:

The point estimation process involves using statistical values ​​derived from sample data to obtain the best estimate of the corresponding unknown parameters of the population. Different methods can be used to compute the point estimator, and each technique has different properties.

Method of Moments:

The method of moments for parameter estimation was introduced in 1887 by the Russian mathematician Pafnuty. Start by collecting known facts about a specific population and then apply it to a sample of that population. The first step is to derive an equation that relates the population moment to the unknown parameter.

MLE (Maximum likelihood estimation):

The maximum likelihood estimation method used for point estimation trails to find the unknown parameters that surge the likelihood function. Take a known model and use the values ​​to compare data sets to find the best fit.

How Point Estimate Calculator Works?

An online point of estimate calculator compute and display the best estimate of unknown population parameter by following steps:

Input:

• First, substitute the number of trials and successes.
• Now, plug in the confidence interval in percentage.
• Click on the calculate button for estimation.

Output:

• Our provides the best point estimate using different formulas.
• It displays z score, MLE, Laplace, Jeffrey, and Wilson estimation in the form of an estimated table.

FAQ:

What is the point estimate for the population mean?

The point estimate of the population parameter is the value used to estimate the population parameter. For example, the sample mean x is the point estimate of the population mean μ.

What is the difference between point and interval estimation?

The point estimate of the population parameter is a single statistical value. On the other hand, statistics use confidence intervals to express the accuracy and uncertainty associated with a particular sampling method.

Conclusion:

Use this online point estimate calculator that quickly determines the best guess of population parameters. The calculator uses different estimation techniques to find the suitable point estimate: Laplace, Jeffrey’s, and Wilson methods.

Reference:

From the source of Wikipedia: Point estimation, Point estimators, Bayesian point estimation, Properties of point estimates.

From the source of Tutorial Points: Best Point Estimation, population parameter, Number of Success, Number of trials, Z-Critical Value.