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• W31121572 abstract "La funcion media de vida residual se utiliza en fiabilidad porque caracteriza la distribucion pero su estimacion con la version muestral puede resultar infactible. Una alternativa robusta es la funcion cuantilica de vida residual, cuya estimacion es factible y su interpretacion mas logica en muchos casos. Como inconveniente, no caracteriza la distribucion. Dadas sus ventajas en la practica, en el Capitulo 2 estudiamos los ordenes cuantilicos de vida residual. Dos variables estan ordenadas segun este orden si sus funciones cuantilicas de vida residual estan ordenadas. Los ordenes definidos en los capitulos 3 y 4 estan basados en la comparacion de funciones cuantilicas de vida residual desde o hasta un cierto instante para todos los cuantiles. Algunas aplicaciones son: comparar productos vencido o durante su periodo de garantia, y comparar articulos usados. Envejecimiento es otro concepto importante en fiabilidad. En la tesis caracterizamos la nocion de envejecimiento ya existente en la literatura y conocida como funcion cuantilica de vida residual decreciente a partir de propiedades del orden cuantilico de vida residual. Tambien definimos nuevas nociones de envejecimiento y damos condiciones necesarias para distribuciones bathtub y bathtub invertida. En el septimo capitulo construimos bandas de confianza bootstrap para la diferencia de dos funciones cuantilicas de vida residual, usando profundidad estadistica, que permiten decidir cuando dos variables estan cerca segun el orden cuantilico de vida residual. En el ultimo resumimos nuestras aportaciones y futuras lineas de investigacion.The mean residual life function is a useful tool in reliability because it characterizes the distribution. However, the mean residual life function may not exit and even when it does it may have some practical shortcomings. An alternative to this function is the percentile residual life function that is more intuitive and that can always be calculated but that does not characterize the distribution. Given its advantages in practical situations, in Chapter 2 we study the percentile residual life orders. Two random variables are ordered with respect to this order if their corresponding percentile residual life functions are ordered. The orders defined in Chapter 3 and 4 are based on the comparison of percentile residual life functions from or until a certain moment for all the percentiles. Some applications of these orders are: the comparison of products after of during initial warranty, and the comparison of used items. Aging is another concept very important in reliability. In this dissertation, we characterize the aging notion already existing in the literature and known as decreasing percentile residual life function by means of some properties of the percentile residual life order. Besides, we define new aging notions and give necessary conditions for bathtub and upside-down bathtub distributions. In Chapter 7 we describe a new procedure we have designed to construct bootstrap confidence bands for the differences of two percentile residual life functions using statistical depth. These bands provide a criteria to conclude whether two random variables are close or not with respect to the percentile residual life order. In the last chapter we summarize the main contributions and explain our future lines of research" @default.
• W31121572 created "2016-06-24" @default.
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• W31121572 date "2009-01-01" @default.
• W31121572 modified "2023-09-26" @default.
• W31121572 title "Stochastic orderings and aging notions based on percentile residual life functions" @default.
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