Estimasi parameter distribusi length biased weighted eksponensial dan length biased weighted weibull

Sabila, Zafira Nur (2020) Estimasi parameter distribusi length biased weighted eksponensial dan length biased weighted weibull. Diploma thesis, UIN Sunan Gunung Djati Bandung.

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Abstract

Abstrak Distribusi berbobot adalah salah satu alternatif distribusi kontinu ketika distribusi normal tidak sesuai dengan tujuan. Karena pada peristiwa atau kejadian saat ini tidak semua data dapat dianalisis menggunakan distribusi normal, misalnya pada data survival atau data daya tahan hidup makhluk hidup. Data survival ini memiliki kemencengan tertentu sehingga apabila dianalisis menggunakan distribusi normal hasilnya tidak sesuai. Distribusi ini terdiri dari dua kasus khusus yaitu distribusi Length Biased dan Size Biased. Skripsi ini memperkenalkan kelas baru dari kasus khusus distribusi berbobot yaitu distribusi Length Biased Eksponensial Berbobot (LBWED) dan Length Biased Weibull (LBWWD). Beberapa karakteristik dari distribusi ini telah ditentukan, seperti mean, variansi, fungsi tahan hidup (Survival) dan fungsi kegagalan (Hazard). Langkah – langkah estimasi parameter distribusi dibuat dengan menggunakan metode Maximum Likelihood Estimation (MLE) dan dibuat program estimasi menggunakan software R untuk membantu perhitungan nilai parameter dari LBWED dan LBWWD. Selanjutnya, untuk menentukan kecocokan model terhadap data yaitu dengan menggunakan metode Akaike Information Criterion (AIC) pada distribusi Length Biased Weighted Eksponensial dan Length Biased Weighted Weibull dengan nilai AIC nya yang terkecil. Abstract Weighted distribution is one of the alternative distribution continous when the normal distribution is not suitable for purpose because in reality, a lot of data whose distribution does not always follow a normal distribution, for example in data failure waiting time. This data has a certain slope so that the normal distribution is less precise if it is still used to model the data. This distribution consists of two special cases namely the bias length distribution and the size of bias. This thesis introduces a new class of special cases of weighted distributions, namely the Length Biased Exponential Weighted (LBWED) and Length Biased Weibull (LBWWD) distributions. Several factors from this distribution have been determined, such as mean, variance, survival function and failure function (Hazard). Estimating steps for parameter distribution are made using the Maximum Likelihood Estimation (MLE) method and a program is made using R software to help calculate the parameter values from LBWED and LBWWD. Furthermore, to determine the best model, using the Akaike Information Criterion (AIC) method in the Length Biased Exponential and Weighted Weibull distribution which is the best value is the best model is the Length Biased Exponential Weighted (LBWED) distribution’s model.

Item Type: Thesis (Diploma)
Uncontrolled Keywords: Distribusi Berbobot; Distribusi Length – Biased Eksponensial Berbobot; Distribusi Length – Biased Weibull Berbobot; Metode Maximum Likelihood Estimation (MLE); Newton – Raphson.
Subjects: Mathematics > Data Processing and Analysis of Mathematics
Applied mathematics > Statistical Mathematics
Divisions: Fakultas Sains dan Teknologi > Program Studi Matematika
Depositing User: Zafira Nur Sabila
Date Deposited: 16 Oct 2020 06:49
Last Modified: 16 Oct 2020 06:49
URI: https://digilib.uinsgd.ac.id/id/eprint/34276

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