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

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

How to Calculate Best Point Estimation - Tutorial