  Here, in this paper it has been considered a sub family of exponential
family. Maximum likelihood estimations (MLE) for the parameter of this family,
probability density function, and cumulative density function based on a sample
and based on lower record values have been obtained. It has been considered
Mean Square Error (MSE) as a criterion for determining which is better in
different situations. Additionally, it has been proved some theories about the
relations between MLE based on lower record values and based on a random
sample. Also, some interesting asymptotically properties for these estimations
have been shown during some theories.
