Parameter:
Q. What is Parameter?
Ans: In Statistical Inference parameter belongs to the population for which estimation is required. In general for a huge population we need to construct a statistics which can be use as a estimate of the population parameter.
$\small E(statistics)= Parameter$
Example: For a normal distribution of $\small X\sim N(\mu,\sigma)$, the parameters are $\small \mu,\sigma$
Statistics:
Q.What is Statistics?
Ans: In statistical inference statistics regarded as an estimate of the parameter from the population. Statistics can be shown as a function of sample observation.
Example: For a normal distribution $\small X\sim N(\mu,\sigma)$, $\small \bar{x}$(sample mean) is the estimate of population mean $\small \mu$.
Parametric Space:
Q. What is parametric space in statistics?
Ans: All possible values of parameters or the range of the parameter is parametric space.It is denoted by $\small \Theta$.
Example:For a normal distribution $\small X\sim N(\mu,\sigma)$, the parametric space is $\small \Theta$=$\small {(\mu,\sigma):-\infty <\mu<\infty,0<\sigma<\infty}$.
Tags: statistical inference, parametric space notation, parametric space symbol, what is parametric space in statitics, parameter space normal distribution