How to Calculate Best Point Estimation - Tutorial

How to Calculate Best Point Estimation - Tutorial, Definition, Formula, Example

Definition:

If the estimate is acquired as a single number, then the estimate is called as a point estimate. This tutorial explains you how to calculate the best point estimation.

Formula:

MLE = S / T Laplace = (S+1) / (T+2) Jeffrey = (S+0.5) / (T+1) Wilson = (S+(z2/2)) / (T+z2) Where, MLE = Maximum Likelihood Estimation S = Number of Success T = Number of Trials z = Z-Critical Value
Best Point Estimation Rules :

1. MLE<=0.5 -- >Wilson Estimation 2. Between MLE>0.5 and MLE<0.9 -- >MLE 3. MLE>0.9 -- > either Laplace or Jeffrey based on which is small.

Example :

If a coin is tossed 4 times out of nine trials in 99% confidence interval level, then what is the best point of success of that coin?

Given :

Success (S) = 4 Trials (T) = 9 Confidence Interval Level (P) = 99% = 0.99

To Find :

Best point estimation

Solution :

Substitute the given values in the formula,

Step1 :
MLE = S / T
= 4 / 9
MLE = 0.4444
Step2 :
Laplace = (S+1) / (T+2)
= (4+1) / (9+2)
= 5 / 11
Laplace = 0.4545
Step3 :
Jeffrey = (S+0.5) / (T+1)
= (4+0.5) / (9+1)
= 4.5 / 10
Jeffrey = 0.45
Step4 :

Find Z-Critical Value from Z table

Z-Critical Value (z) = for 99% level = 2.5758
Wilson = (S+(z2/2)) / (T+z2)
= (4+(2.57582/2)) / (9+2.57582)
Wilson = 0.468
Result :

Thus the Best Point Estimation is 0.468 as MLE<=0.5

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