Aim: This study aims to correct undercounts in cancer data before initiating a population-based cancer registry program, employing an innovative Bayesian methodology. Background: Underestimation is a widespread issue in cancer registries within developing countries. Methods: This secondary study utilized cancer registry data. We employed the Bayesian approach to correct undercounting in cancer data from 2005 to 2010, using the ratio of pathology to population-based data in the Golestan province as the initial value. Results: The results of this study showed that the lowest percentage of undercounting belonged to Khorasan Razavi province with an average of 21% and the highest percentage belonged to Sistan and Baluchestan province with an average of 38%. The average age-standardized incidence rate (ASR) for all provinces of the country except Golestan province was equal to 105. 72 (Confidence interval (CI) 95% 105. 35-106. 09) per 100, 000 and after Bayesian correction was 137. 17 (CI 95% 136. 74-137. 60) per 100, 000. In 2010 the amount of ASR before Bayesian correction was 100. 28 (CI 95% 124. 39-127. 09) per 100, 000 for women and 136. 49 (CI 95% 171. 20-174. 38) per 100, 000 for men. Also, after implementing the Bayesian correction, ASR increased to 125. 74 per 100, 000 for women and 172. 79 per 100, 000 for men. Conclusion: The study demonstrates the effectiveness of the Bayesian approach in correcting undercounting in cancer registries. By utilizing the Bayesian method, the average ASR after Bayesian correction with a 29. 74 percent change was 137. 17 per 100, 000. These corrected estimates provide more accurate information on cancer burden and can contribute to improved public health programs and policy evaluation. Furthermore, this research emphasizes the suitability of the Bayesian method for addressing underestimation in cancer registries. It also underscores its pivotal role in shaping the trajectory of future investigations in this field

The reliability function‎, ‎or the survival function at a specified time t‎, ‎denotes the proportion of products that remain operational beyond time t and continue to function‎. ‎This interpretation underscores the pivotal role of the survival function and its estimation in understanding lifetime phenomena‎. ‎This paper explores the estimation of the survival function for the inverse Lindley distribution based on lower records‎. ‎The estimation techniques encompass maximum likelihood and bootstrap methods‎. ‎Furthermore‎, ‎Bayesian approaches employing Metropolis-Hastings and importance sampling algorithms are employed‎. ‎In addition to deriving approximate confidence intervals using the delta method and percentile bootstrap intervals for the survival function‎, ‎Chen and Shao's shortest width credible intervals are also determined‎. ‎A comprehensive simulation study is presented to assess the effectiveness of both point and interval estimators‎. Finally‎, ‎an application of the results is given to a real data set.

Descriptive statistics is the process of summarizing gathered raw data from a research and creating useful statistics, which help the better understanding of data. According to the types of variables, which consist of qualitative and quantitative variables, some descriptive statistics have been introduced. Frequency percentage is used in qualitative data, and mean, median, mode, standard deviation; standard error, variance, and range are some of the statistics which are used in quantitative data. In health sciences, the majority of continuous variables follow a normal distribution. skewness and kurtosis are two statistics which help to compare a given distribution with the normal distribution.