Relations for single and product moments of record values from Gumbel distribution

Exponential Lomax Distribution

“…Some details about the Lomax distribution and Pareto family are given by Arnold [4] and Johnson et al [20]. Some properties and moments for the Lomax distribution have been discussed by Ahsanullah [2], Amin [3], Balakrishnan [6] and Lee et al [22]. In the literature, some extensions of the Lomax distribution are available such as the exponentiated Lomax (EL) by Abdul-Moniem [1], Marshall-Olkin extended-Lomax (MOEL) by Ghitany et al [14] and Gupta et al [16], betaLomax (BL), Kumaraswamy-Lomax (KwL), McDonaldLomax (McL) by Lemonte et al [23] and gamma-Lomax (GL) by Cordeiro et al [12].…”

An Analysis of Record Statistics based on an Exponentiated Gumbel Model

“…A record model is closely related to models of order statistics; in addition, both appear in many statistical applications that are widely used in statistical modeling and inferences because they can be viewed as order statistics from a sample whose size is determined by the value and order of the occurrence of observations. In particular, Balakrishnan et al (1992) established some recurrence relationships for single and double moments of lower record values from the Gumbel distribution. Jaheen (2003) derived Bayes estimators of unknown parameters of the Gompertz distribution based on upper record values and obtained prediction bounds for future upper record values.…”

Estimation for generalized half logistic distribution based on records

“…A record model is closely related to the model of order statistics, and both are widely employed in statistical applications as well as in statistical modeling and inferences because they can be viewed as order statistics from a sample whose size is determined by the value and order of the occurrence of observations. In particular, Balakrishnan et al (1992) established some recurrence relationships for single and double moments of lower record values from the Gumble distribution. Recently, Ahmadi and Balakrishnan (2011) discussed the prediction of future order statistics based on the largest and smallest observations when there is a new record.…”