An extension of the half-normal distribution

Generalized variable method inference for the location parameter of the general half-normal distribution

“…As n −→ ∞, −1 ( 1 2 + 1/2n) −→ 0, and thus for moderate to large sample sizes there will be little difference betweenτ andτ BC , and hence the intervals for ζ obtained using Equations (7) and (8) will also differ only marginally. For small-sized samples, these differences will generally be more pronounced.…”

“…Wiper et al [12] noted that the Bayesian posterior mean estimator happened to be identical to this value. Pewsey [10] also noted that nominally two-sided 95% non-bias-corrected confidence interval calculated using Equation (7) and BC confidence interval calculated using Equation (8) for ζ are identical to two decimal places, the common interval being (5.41,5.63). Wiper et al [12] noted, when re-analyzed the same fat data, that the Bayesian HPD interval calculated using Equation (11) for ζ is (5.44,5.63).…”

“…ML point estimates of the location and scale parameters of an assumed half-normal distribution are, respectively,ζ obs = y (1) = 0.0000, ζ BC obs = 1.5073. Also noted that nominally two-sided 95% non-bias-corrected confidence interval calculated using Equation (7) and BC confidence interval calculated using Equation (8) for ζ are identical to two decimal places, the common interval being (0.00,2.68). When analyzed these data, the Bayesian HPD interval calculated using Equation (11) for ζ is (0.00,2.44).…”

“…Beta generalized half-normal distribution has been proposed by Pescim et al [7] As an extension to the existing half-normal distribution, the slashed half-normal distribution was recently introduced by Olmos et al [8] The Kumaraswamy generalized half-normal distribution for skewed positive data was suggested by Cordeiro et al [9] Classical inference for the halfnormal has been discussed by Pewsey. [10,11] Bayesian inference for the half-normal and half-t distributions have been discussed by Wiper et al [12] Measurement error using the half-normal distribution has been discussed by Bland.…”

Estudio de simulación para comparar varios estimadores de varianza en el marco de la regresión no paramétrica

“…Las distribuciones asimétricas se definen a partir de una variable que se distribuye semi-normal, definida como el valor absoluto de una variable que se distribuye normal estándar (Olmos et al 2012). En ambos casos el procedimiento empleado centra las distribuciones semi-normales en 0, pero mantiene una de ellas asimétrica a la derecha y la otra a la izquierda (ver Figura 1).…”