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Martínez Carlos / Revista Ingeniería UC , Vol. 23, No. 1, Abril 2016, 1-7 3 2.3. PSH estimator (2001) Peña et al. [5] developed a non-parametric estimator of the survival function to estimate the survival function of recurrent events. The nonparametric estimator of the inter-event time survivor functions under the assumption of a renewal. They consider a structure model which gap-times independent and identical distribution (i.i.d.). The author used two counting processes N and Y. they considered two time scales: one related to calendar time (s) and other related to gap time (t). So, ∏ S (s, t) = w≤t [ 1 − ] ∆N (s, w) Y (s, w) (5) where, S (t, s) is the estimator of survival analysis, N(s, w) is one counting process and represents the number of observed events in the calendar period [0,s] with t≤w. It is calculated as, And, N (s, t) = K i (s) = n∑ K∑ i (s) I { T ij ≤t } (6) i=1 j=1 n∑ I { T ij ≤s } (7) i=1 The function {.} is one if the condition on breakers is true and zero in other case. Y(s, w) is other counting processes and represents the number of observed events in the period [0, s] with t≥w. So, ⎡ n∑ Y (s, t) = ⎢⎣ K∑ i (S −) j=1 3. Proposals i=1 I { T i j ≥ t } + I { min(s, τ i ) − S iKi (S −) ≥ t } ⎤⎥⎦ (8) We designed two functions in R language. We designed “Counting.Processes.WC” and “Counting.Processes.PSH” function to calculate of the counting processes of WC and PSH. With the help of the functions, the users can be able of to plot the occurrences of an event for number of wished units. The user can change the total units to plot. We do not show the routines of these functions on this work. However, they can be solicited way e-mail of the author. The author included these functions on library of a new version of TestS urvRec package of R − CRAN. 3.1. Counting.Processes.WC function This function permits estimates the counting processes of WC estimator and permits to plot the occurrences of events for a number wished of study units. The syntaxes of this function is, Counting.Processes.WC
4 Martínez Carlos / Revista Ingeniería UC , Vol. 23, No. 1, Abril 2016, 1-7 the plot. For defect is “blue”, colcensor
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