The inductive inference may be termed as the logic of drawing statistically valid
conclusions about the population characteristics on the basis of a sample drawn
from it in a scientific manner. We know the utility of sample method over complete
enumeration (census) method and described the various sampling techniques of
obtaining representative samples from the population. In this, we shall develop the
technique which enables us to generalize the results of the sample to the
population; to find how far these generalizations are valid, and also to estimate the
population parameters along with the degree of confidence. The answers to these
and many other related problems are provided by a very important branch of
statistics, known as Statistical Inference.
Parameter The statistical constant of the population like mean (μ), variance(σ2
),
skewness (ß1), kurtosis (ß2), moments (μr), correlation coefficient (ῤ) etc. are
known as parameters. Obviously, parameters are function of the population values.
Generally, the population parameters are unknown and their estimates provided by
the appropriate sample statistics are used.
Parameter Space: Let us consider a random variable X with probability density
function P.d.f f(x,θ). In most common applications, though not always, the
functional form of the population distribution is assumed to be known except for
the value of some unknown parameters θ which may take any value on a set ϴ.
This is expressed by writing the p.d.f in the form f(x,θ),θ ϵ ϴ.The set ϴ, which is
the set of all possible values of θ is called the parameter space
