This study proposes a non-parametric estimation method of the survival probability for road facilities using arbitrarily left-truncated, right-censored and interval censored data. Traditionaly, several studies have been proposed on the estimation of the survival probability especially in the medical and statistical fields. Although they deal with truncated and censored data, all of them assume that the left truncated time, a period from the survival start time to measurement start time, is known. However, for road facilities, once we miss the facility installation time, it is difficult to find the survival start time afterwards. Also, some studies assume the truncation and censoring timings are random. However, actual truncation and censoring timimings may not be perfectly random. Therefore, this study theoretically proposes an estimation method of the survival probability without knowing the truncated time using arbitrarily truncated, censored data; and validates the method using hypothetical data.
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