It is known that energy subiect has ocuppied a lot of scientests minds about
how to treat the traditional energy and the renewing energy . we know that
most traditional energy coal , oil , Natural gas, neuclear fuel , are limited
guantiy and alsow subjected to be ended .Statics studies refer to reserve
of oil in world will exhausted btween ( 2075- 2100) and alsow cosl too .
While neuclear fuerl which the world seek today through explod the uranium
atom ( 233) the therum atom (239) and neuclear mxied through ruemlear
mixing , These energy have effect on environment and humanity speciaty if
they are used in militery purposes .
For all theses scientests srarch for resources of renewing enery through
researches

Survival analysis is one of the types of data analysis that describes the time period until the occurrence of an event of interest such as death or other events of importance in determining what will happen to the phenomenon studied. There may be more than one endpoint for the event, in which case it is called Competing risks. The purpose of this research is to apply the dynamic approach in the analysis of discrete survival time in order to estimate the effect of covariates over time, as well as modeling the nonlinear relationship between the covariates and the discrete hazard function through the use of the multinomial logistic model and the multivariate Cox model. For the purpose of conducting the estimation process for both the discrete

Iraq within the ranks of the fledgling communities characterized by a broad base of the population pyramid, because they pose the age group (under 15 years) of a large proportion of the community, as it exceeded the proportion (40%) during the years of research extended (1986-2010) Despite the relative decline in the rates fertility during that period, but the proportion of young people remained high, especially for groups of at least five years, amounting to about 14% in 2012, a little more than the proportion of what constitutes age group (5-9 above) years, where it was (13%) and this naturally predicts continuing population increases in coming decades, due to the entry of those numbers of individuals in the reproductive stage,

Praise be to God, Lord of the worlds, and prayers and peace be upon our master Muhammad and upon his family and companions as a whole.
    The topic of attention was drawn to the attention of the speakers, as it made me ponder it carefully, and my goal in that is to know the reason for the interest of the speakers and their care for it, and to clarify from their books the purpose of making this topic one of the advanced investigations with them.

     The idea of ​​writing a paper on the subject of consideration was not absent from my thinking, because I saw the attention of speakers on this issue, as they made it one of the first issues that they deal with studying in their work

Exponential distribution is one of most common distributions in studies and scientific researches with wide application in the fields of reliability, engineering and in analyzing survival function therefore the researcher has carried on extended studies in the characteristics of this distribution.

In this research, estimation of survival function for truncated exponential distribution in the maximum likelihood  methods and Bayes first and second method, least square method and Jackknife dependent in the first place on the maximum likelihood method, then on Bayes first method then comparing then using simulation, thus to accomplish this task, different size samples have been adopted by the searcher us