Best Point Estimation

Point estimation involves the use of sample data to calculate a single value (known as a statistic) which is to serve as a "best guess" or "best estimate" of an unknown (fixed or random) population parameter. More formally, it is the application of a point estimator to the data.

Formula

MLE=STMLE=ST

Laplace=S+1T+2Laplace=S+1T+2

Jeffrey=S+0.5T+1Jeffrey=S+0.5T+1

Wilson=S+z22T+z2Wilson=S+z22T+z2

Where −

· MLEMLE = Maximum Likelihood Estimation.

· SS = Number of Success .

· TT = Number of trials.

· zz = Z-Critical Value.

Example

Problem Statement:

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?

Solution:

Success(S) = 4 Trials (T) = 9 Confidence Interval Level (P) = 99% = 0.99. In order to compute best point estimation, let compute all the values:

Step 1

MLE=ST=49,=0.4444MLE=ST=49,=0.4444

Step 2

Laplace=S+1T+2=4+19+2,=511,=0.4545Laplace=S+1T+2=4+19+2,=511,=0.4545

Step 3

Jeffrey=S+0.5T+1=4+0.59+1,=4.510,=0.45Jeffrey=S+0.5T+1=4+0.59+1,=4.510,=0.45

Step 4

Discover Z-Critical Value from Z table. Z-Critical Value (z) = for 99% level = 2.5758

Step 5

Wilson=S+z22T+z2=4+2.57582229+2.575822,=0.468Wilson=S+z22T+z2=4+2.57582229+2.575822,=0.468

Result

Accordingly the Best Point Estimation is 0.468 as MLE ≤ 0.5