A useful subfamily of the exponential family is considered. The ML estimation based on upper record values are calculated for the parameter, Cumulative Density Function, and Probability Density Function of the subfamily. The relationship between MLE based on record values and a random sample are discussed, along with some properties of these estimators, and its utility is shown for large samples.
Hosseini, S., Nasiri, P., & Gore, S. D. (2019). Maximum likelihood estimations based on upper record values for probability density function and cumulative distribution function in exponential family and investigating some of their properties. Journal of Modern Applied Statistical Methods, 18(2), eP2731. doi: 10.22237/jmasm/1604189100