This study examines the citation distribution of scientific papers using two large data sets: 783,339 papers published in 1981 (ISI data) and 24,296 papers from Physical Review D (PRD data). The results show that the citation distribution for highly-cited papers follows a power-law decay, $ N(x) \sim x^{-\alpha} $, with $ \alpha \approx 3 $. This is supported by a Zipf plot, which indicates a power-law dependence for leading rank papers with an exponent close to -1/2. However, the distribution is not described by a single function over the entire range of citation counts. The data shows that the citation distribution has a stretched exponential form for lower citation counts but deviates for higher citation counts, where the distribution is sparse and difficult to fit with a smooth function. The study also highlights the difference between minimally-cited and heavily-cited papers, with the former having a short lifetime and the latter being influenced by collective effects. The citation distribution of PRD papers published in different time periods shows that the citation count of highly-cited papers decreases over time, indicating that the citation distribution is still evolving. The study concludes that the citation distribution has a power-law tail with exponent close to 3, differing from previous claims of a stretched exponential form. The results suggest that the citation distribution is complex and not described by a single function, and that further research is needed to fully understand the citation behavior of scientific publications.This study examines the citation distribution of scientific papers using two large data sets: 783,339 papers published in 1981 (ISI data) and 24,296 papers from Physical Review D (PRD data). The results show that the citation distribution for highly-cited papers follows a power-law decay, $ N(x) \sim x^{-\alpha} $, with $ \alpha \approx 3 $. This is supported by a Zipf plot, which indicates a power-law dependence for leading rank papers with an exponent close to -1/2. However, the distribution is not described by a single function over the entire range of citation counts. The data shows that the citation distribution has a stretched exponential form for lower citation counts but deviates for higher citation counts, where the distribution is sparse and difficult to fit with a smooth function. The study also highlights the difference between minimally-cited and heavily-cited papers, with the former having a short lifetime and the latter being influenced by collective effects. The citation distribution of PRD papers published in different time periods shows that the citation count of highly-cited papers decreases over time, indicating that the citation distribution is still evolving. The study concludes that the citation distribution has a power-law tail with exponent close to 3, differing from previous claims of a stretched exponential form. The results suggest that the citation distribution is complex and not described by a single function, and that further research is needed to fully understand the citation behavior of scientific publications.