ESTIMASI DAN UJI HIPOTESIS MEDIAN PADA DISTRIBUSI EKSPONENSIAL

AULIA PUTRI RAHMAWATI, . (2026) ESTIMASI DAN UJI HIPOTESIS MEDIAN PADA DISTRIBUSI EKSPONENSIAL. Sarjana thesis, UNIVERSITAS NEGERI JAKARTA.

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Abstract

Median merupakan ukuran pemusatan yang lebih robust dibandingkan mean karena tidak mudah dipengaruhi oleh pencilan, sehingga lebih representatif untuk data yang menceng seperti distribusi eksponensial. Namun, prosedur inferensia statistik yang secara khusus dikembangkan untuk median pada distribusi eksponensial masih terbatas. Penelitian ini bertujuan mengestimasi median, mengonstruksi interval konfidensi, dan mengembangkan prosedur uji hipotesis untuk median pada distribusi eksponensial. Estimator median diperoleh menggunakan metode Maximum Likelihood Estimation (MLE) melalui sifat invarian, sehingga diperoleh (\hat{m}=\bar{X}ln{2}). Distribusi sampling estimator median diturunkan melalui hubungan distribusi eksponensial, Gamma, dan chi-square, yaitu (2n\hat{m}/m\sim\chi^2\left(2n\right)), yang digunakan sebagai dasar pembentukan interval konfidensi dan uji hipotesis. Ilustrasi menggunakan data simulasi dengan \left(\theta=1\right) dan \left(n=50\right) menghasilkan estimasi median sebesar 0,6847, mendekati median populasi sebesar 0,6931. Interval konfidensi 95% sebesar (0,5285;\ 0,9225) mencakup nilai median populasi, sedangkan hasil uji hipotesis memberikan keputusan yang konsisten dengan hasil estimasi. Hasil penelitian menunjukkan bahwa prosedur estimasi, interval konfidensi, dan uji hipotesis yang dikembangkan dapat digunakan sebagai inferensia statistik untuk median pada distribusi eksponensial. ***** The median is a more robust measure of central tendency than the mean, as it is less affected by outliers, making it more representative for skewed data such as data following the exponential distribution. However, statistical inference procedures specifically developed for the median of the exponential distribution remain limited in the literature. This study aims to estimate the median, construct its confidence interval, and develop a hypothesis testing procedure for the median of the exponential distribution. The median estimator was obtained using the Maximum Likelihood Estimation (MLE) method through the invariance property, resulting in (\hat{m}=\bar{X}ln{2}). The sampling distribution of the median estimator was derived from the relationship among the exponential, Gamma, and chi-square distributions, namely (2n\hat{m}/m\sim\chi^2\left(2n\right)), which served as the basis for constructing the confidence interval and hypothesis test. An illustration using simulated data with \theta\ =\ 1 and n\ =\ 50 yielded a median estimate of \hat{m}=0.6847, close to the population median of 0.6931. The 95% confidence interval of (0.5285;\ 0.9225) successfully covered the population median, while the hypothesis testing result was consistent with the estimation outcome. The results indicate that the developed estimation, confidence interval, and hypothesis testing procedures can be used as statistical inference tools for the median of the exponential distribution.

Item Type:	Thesis (Sarjana)
Additional Information:	1). Prof. Dr. Suyono, M.Si 2). Faroh Ladayya, M.Si
Subjects:	Sains > Statistika
Divisions:	FMIPA > S1 Statistika
Depositing User:	Users 35427 not found.
Date Deposited:	12 Aug 2026 04:35
Last Modified:	12 Aug 2026 04:35
URI:	http://repository.unj.ac.id/id/eprint/70284

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