الفهرس 
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Abstract
The statistical analysis of time-to-event data shows a main role in many of various application areas such as, industrial (reliability testing), medical (survival analysis), and demographic (migration analysis, life events research). The hazard rate is used greatly as a methodological tool in these types of usages to define the instantaneous risk of observing the event of interest over time.
The main objective of this thesis is to enrich the nonparametric estimation of the hazard function using trimmed linear moments The population hazard function (which indicated the approximation of hazard quantile function) is approximated using a nonparametric methodology based on the TL-moments and the orthogonal Jacobi polynomial as an approximation. This methodology has the capacity to acquire more information regarding the data’s arbitrary distribution. This method is focused on reducing the sum absolute error between the population hazard quantile function and its portrayal in TL-moments.
Unlike its parametric counterpart, there is no need to make any assumptions about the underlying distribution. We also used symmetric and asymmetric distributions to demonstrate the benefits of the suggested technique. and compare it other nonparametric method.
As the basis of our comparisons, we simulated 50,100, and150 observations from Pareto, Gamma, Log normal, normal, uniform and Weibull distributions
and applicated real data (155patients with Stomach Tumors) We take the hazard quantile function which have Min∑▒|e(u)| .
In the same time, best fitting to distribution. In addition, we will compare this new approximation of the hazard quantile with the corresponding histogram and kernel density.
when we compared the hazard estimators of distributions with trimmed linear moment and kernel by e(u) we found that TL-moment give smallest value compared to kernel.