Analisis distribusi Exponentiated Discrete Lindley dengan kendala data overdispersi pada data masa hidup pasien covid-19

Musvira, Lesta Milva (2021) Analisis distribusi Exponentiated Discrete Lindley dengan kendala data overdispersi pada data masa hidup pasien covid-19. Sarjana thesis, UIN Sunan Gunung Djati Bandung.

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Abstract

INDONESIA : Distribusi Exponentiated Discrete Lindley adalah salah satu distribusi peluang diskrit yang digunakan untuk menganalisis data waktu hidup dan dapat memodelkan data yang mengalami overdispersi. Overdispersi merupakan keadaan dimana nilai variansi dari distribusi data lebih besar dari nilai rata-ratanya. Skripsi ini memperkenalkan distribusi peluang diskrit baru yaitu Distribusi Exponentiated Discrete Lindley. Beberapa karakteristik dari distribusi ini telah ditentukan, seperti ekspektasi, variansi, skewness, kurtosis, fungsi tahan hidup dan fungsi hazard. Langkah-langkah estimasi parameter distribusi ditentukan menggunakan metode Maximum Likelihood Estimation dengan pendekatan metode Newton-Raphson. Pengujian overdispersi dilakukan dengan Uji Deviance untuk menentukan terjadinya overdispersi pada data. Adapun pengujian signifikansi parameter menggunakan Uji Rasio Likelihood untuk mengetahui pengaruh parameter distribusi secara signifikan. Selanjutnya, untuk menentukan kecocokan model distribusi terhadap data menggunakan metode Akaike Information Criterion. Studi kasus dilakukan pada data lamanya perawatan 60 pasien COVID-19. Hasil dari penelitian ini menyatakan bahwa diperoleh nilai estimasi untuk masing-masing parameter dan parameter distribusi berpengaruh signifikan terhadap model, sementara data lamanya perawatan 60 pasien COVID-19 mengalami overdispersi sehingga dari uji kecocokan model Distribusi Exponentiated Discrete Lindley sesuai terhadap data lamanya perawatan pasien COVID-19. ENGLISH : Exponentiated Discrete Lindley Distribution is one of the discrete probability distributions used to analyze life time data and can model overdispersion data. Overdispersion is a condition where the variance value of the data distribution is greater than the average value. This thesis introduces a new discrete probability distribution, namely the Exponentiated Discrete Lindley Distribution. Several characteristics of this distribution have been determined, such as expectation, variance, skewness, kurtosis, survival function and hazard function. The steps to estimate the distribution parameters are determined using the Maximum Likelihood Estimation method with the Newton-Raphson method approach. Overdispersion testing is done by Deviance Test to determine the occurrence of overdispersion in the data. The parameter significance test uses the Likelihood Ratio Test to determine the effect of the distribution parameters significantly. Furthermore, to determine the suitability of the distribution model to the data using the Akaike Information Criterion method. The case study was conducted on data on the length of treatment for 60 COVID-19 patients. The results of this study state that obtained the estimated value for each parameter and the distribution parameters have a significant effect on the model, while the length of treatment data for 60 COVID-19 patients is overdispersed so that from the model fit test the distribution Exponentiated Discrete Lindley is in accordance with data on the length of treatment for COVID-19 patients.

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