An Overview of Asymptotic Properties of Estimators in Truncated Distributions

Normal and Student´s t Distributions and Their Applications

“…Statistical methods dealing with the properties and applications of the half-normal distribution have been extensively used by many researchers in diverse areas of applications, particularly when the data are truncated from below (that is, left truncated,) or truncated from above (that is, right truncated), among them Dobzhansky and Wright (1947), Meeusen and van den Broeck (1977), Haberle (1991), Altman (1993), Buckland et al (1993) , Chou and Liu (1998), Klugman et al (1998), Bland and Altman (1999), Bland (2005), Goldar and Misra (2001), Lawless (2003), Pewsey (2002Pewsey ( , 2004, Chen and Wang (2004) and Wiper et al (2005), Babbit et al (2006), Coffey et al (2007), Barranco-Chamorro et al (2007), and Cooray and Ananda (2008), are notable. A continuous random variable X is said to have a (general) half-normal distribution, with parameters μ (location) and σ (scale), that is, X |μ, σ → H N (μ, σ ), if its pdf f X (x) and cdf F X (x) = P(X ∈ x) are, respectively, given by…”

A Generalized Rayleigh Family of Distributions Based on the Modified Slash Model

“…Some of these results follow directly from (8) under certain reparameterizations, while other ones follow taking the limit when q → ∞. Similar to the techniques used in [25], the limit distribution of (1) when q → ∞ is obtained. Lemma 1.…”

A Family of Truncated Positive Distributions

“…The half-normal (HN) model is a member of this family, which was studied in detail by Pewsey [5,6]. Some extensions of the HN distribution have been introduced by Chou and Liu [7], Barranco-Chamorro et al [8], Cooray and Ananda [9] and Olmos et al [10], among others. Other authors who have developed extensions of distributions contained in the HS family are Balakrishnan and Puthenpura [11] for the half-logistic (HL) distribution, Wiper et al [12] for the HN and half-t (Ht) distributions, Polson and Scott [13] for the half-Cauchy (HC) distribution and Gui [14] for the half-power exponential (HPE) distribution, among others.…”