# Parametric inference

## An Overview

Parametric inference is the process by which information from sample data is used to draw conclusions about the population properties from which the sample was selected. The distribution of the population from which sample is drawn is assumed to be known and can be modeled by a probability distribution that have a fixed set of parameters. Suppose we want to analyze the compressive strength of concrete. There is natural variability in the strength of each individual concrete specimen. Therefore, we are interested in estimating the variability of comprehensive strength in this population. The objective is to approximate the value of parameter on the basis of a sample statistic. For example, the sample mean $\bar{X}$ (statistic) is used to estimate the population mean $\mu$ (parameter). A measure of the population like its mean, variance, standard deviation, etc., calculated on the basis of population values is called a parameter. Population parameters are denoted by Greek letters, e.g., $\mu, ~ \sigma^2, ~ \sigma$, etc. A measure computed on the basis of sample values only is called a statistic. For example, $Y = \sum\limits_{i=1}^nx_i$ is a statistic. An estimator is a statistic obtained by a specified procedure for estimating a population parameter. It is a random variable, as its value differs from sample to sample and the samples are selected with specified probabilities. The particular value, which the estimator takes for a given sample is known as an estimate. For more information click here.