PENGGUNAAN RUMUS STIRLING DAN FUNGSI PEMBANGKIT MOMEN PADA PROSES PEMBUKTIAN DISTRIBUSI NORMAL SEBAGAI PENDEKATAN DISTRIBUSI BINOMIAL

Raden Gunawan Santosa; Nugroho Agus Haryono

doi:10.20527/epsilon.v18i2.14164

PENGGUNAAN RUMUS STIRLING DAN FUNGSI PEMBANGKIT MOMEN PADA PROSES PEMBUKTIAN DISTRIBUSI NORMAL SEBAGAI PENDEKATAN DISTRIBUSI BINOMIAL

Raden Gunawan Santosa, Nugroho Agus Haryono

Abstract

Research in mathematics and statistics can be categorized into two main types: analytical-theoretical research and applied-practical research, both of which make significant contributions to statistical analysis. This research is particularly relevant to the analysis of large-scale binary variables, where the binomial distribution is often used as the basis for computation. In such cases, the normal distribution can serve as an approximation to the binomial distribution, reducing the complexity of calculations. This study aims to demonstrate that the normal distribution can be used as an approximation for the binomial distribution. Two proof methods are presented: one utilizing the moment-generating function and the other employing Stirling's formula. The methodology involves a literature review by gathering and analyzing various relevant references. The findings indicate that as the value of 𝑛 n increases, the difference between calculations using the binomial and normal distributions approaches zero exponentially.

Keywords

Binomial distribution; Normal distribution;moment generating function;Stirling formula

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DOI: https://doi.org/10.20527/epsilon.v18i2.14164