New adjustment procedure for distortion in age distribution

To solve this problem, Gupta (1975) proposed some “more general method” for the correction of age misreporting in the census data but as the age gap between the age structures widens, the approach faces an increasing difficulty of the inconsistency of the results with the underlying assumptions. [...] The digit weights 𝛼𝑖𝑗 were used to the observed reported age distribution to find the matrix of true age distribution 𝑊𝑖𝑗 with the elements 𝑊 = 𝛼 𝑊𝑜𝑥𝑦 𝑥𝑦 𝑥 Where 𝑊𝑜𝑥 is the observed number of women at each age and 𝑊𝑥𝑦 is the number of women who reported age x but had true age y, and 𝛼𝑥𝑦 is the probability that a woman with true age y while reporting her age as x. [...] The method is based on the probabilities of terminal digits of the reported age at the time of the data collection. [...] The digit weights 𝑤𝑖𝑗 were used to the observed reported age distribution to find the matrix of true age distribution 𝐼𝑖𝑗 with the elements 𝐼𝑥𝑦 = 𝑤 𝐼𝑜𝑥𝑦 𝑥 Where 𝐼𝑜𝑥 is the observed number of Individuals at each age x and 𝐼𝑥𝑦 is the number of Individuals who reported age x but have true age y, and 𝑤𝑥𝑦 is the probability that an individual with true age y while reporting his/. [...] The quality of the age and sex data of the Republic of Korea and its provinces, 1970 and 1995.