The Type I Generalized Half-Logistic Distribution Based on Upper Record Values

Abstract

We consider the type I generalized half-logistic distribution and derive some new explicit expressions and recurrence relations for marginal and joint moment generating functions of upper record values. Here we show the computations for the first four moments and their variances. Next we show that results for record values of this distribution can be derived from our results as special cases. We obtain the characterization result of this distribution on using the recurrence relation for single moment and conditional expectation of upper record values. We obtain the maximum likelihood estimators of upper record values and their confidence intervals. Also, we compute the maximum likelihood estimates of the parameters of upper record values and their confidence intervals. At last, we present one real case data study to emphasize the results of this paper.

The exponentiated burr xii distribution: moments and estimation based on lower record values

“…and hence the result given in (12). (12), we deduce the recurrence relation for single moments of lower record values from the EB XII distribution.…”

“…Proof: The necessary part follows immediately from equation (12). On the other hand if the recurrence relation in equation (21) is satisfied, then on using equation (1), we have…”

“…Many scientists specially the statisticians have become interested in record values over the past 60 years or so since 1952 when Chandler (1952) first studied the distributions of lower records, record times and inter-record times for iid sequences of random variables. There are hundreds of papers and several books published on record-breaking data and its distributional properties see, for instance, Chandler (1952), Feller (1966), Resnick (1973), Shorrock (1973), Glick (1978), Nevzorov (1987), Balakrishnan and Ahsanullah (1995), , Kumar (2012Kumar ( , 2015Kumar ( , 2016, Kumar and Kulshrestha (2013) and Kumar and Saran (2014), Kumar et al (2015) and so on.…”

k-th rekord values from Dagum distribution and characterization

“…Theory of record values and its distributional properties have been extensively studied in the literature, Ahsanullah [13], Balakrishnan and Ahsanullah [15,16,17], Balakrishnan et al [18], Grudzień and Szynal [24], Arnold et al [1,2], Kumar [7] and Kumar et al [8]. Pawlas and Szynal [19,20] and Saran and Singh [10] have established recurrence relations for single and product moments of kth record values from Weibull, Gumbel and linear exponential distribution.…”

Upper Record Values from Extended Exponential Distribution

“…Recurrence relations for single and product moments of k record values from Weibull, Pareto, generalized Pareto, Burr, exponential, and Gumble distribution are derived by Pawlas and Szynal (1998, 1999, 2000. Kumar (2015Kumar ( , 2016, Kumar, Jain, and Gupta (2015), and Kumar, Kumar, Saran, and Jain (2017) established recurrence relations for moments of k th record values for generalized UPPER RECORD VALUES 4 Rayleigh, Dagum, type-I generalized half logistic, and Kumaraswamy-Burr III distribution, respectively.…”