Parameter Estimation In Statistics

Inferential Statistics :

The two main methods used in inferential statistics are:

1.       Parameter estimation

2.       Hypothesis testing

Parameter Estimation

a)      In estimation, a sample is used to estimate a parameter and to construct a confidence interval around the estimated parameter.

b)      Point estimates are used to estimate the parameter of interest.

c)       The mean (μ) and standard deviation (σ) are the most commonly used point estimates the population means (μ) and standard deviation (σ) are estimated using sample average (j) and standard deviation (sj), respectively.

d)      A point estimate, by itself, does not provide enough information regarding variability encompassed in the simulation response (output measure). This variability represents the differences between the point estimates and the population parameters. Hence, an interval estimate in terms of a confidence interval is constructed using the estimated average (j) and standard deviation (sj).

e)      A confidence interval is a range of values that has a high probability of containing the parameter being estimated.

f)       For example, the 95% confidence interval is constructed in such a way that the probability that the estimated parameter is contained with the lower and upper limits of the interval is 95%. Similarly, 99% is the probability that the 99% confidence interval contains the parameter.

g)      The confidence interval is symmetric about the sample mean j. If the parameter being estimated is μ, for example, the 95% confidence interval constructed around an average of 1 = 28.0 is expressed as follows: 25.5 ≤ μ ≤ 30.5

h)      This means that we can be 95% confident that the unknown performance mean (μ) falls within the interval (25.5, 30.5).

i)        Three statistical assumptions must be met in a sample of observations to be used in constructing the confidence interval. The observations should be normally, independently, and identically distributed:

1.       Observations are identically distributed through the entire duration of the process (i.e., they are stationary or time invariant).

2.       Observations are independent, so that no interdependency or correlation exists between consecutive observations.

3.       Observations are normally distributed (i.e., have a symmetric bell shaped probability density function).

j)        Thus, the simulation data collected are used to contradict the null hypothesis, which may result in its rejection