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"Data lifetime merupakan data yang berisi lama waktu hidup suatu individu ataupun suatu produk yang diukur dari awal waktu penelitian hingga terjadinya suatu event. Salah satu distribusi yang sering digunakan untuk analisis data lifetime adalah distribusi Weibull karena memiliki bentuk fungsi hazard konstan, naik, dan turun. Akan tetapi, terdapat data lifetime dengan bentuk fungsi hazard lain yaitu bentuk unimodal. Oleh karena itu, dilakukan pengembangan distribusi Weibull menggunakan metode compounding sehingga menghasilkan distribusi Weibull-Geometrik (WG) yang dapat memodelkan data lifetime dengan bentuk fungsi hazard unimodal. Pada kenyataannya, terdapat data lifetime yang berbentuk diskrit (count data). Oleh karena itu, pada skripsi ini dibahas pembentukan distribusi yang dapat memodelkan data lifetime diskrit, yang diperoleh dengan cara melakukan diskritisasi pada distribusi WG kontinu. Diskritisasi yang dilakukan yaitu dengan mempertahankan salah satu karakteristik yang dimiliki distribusi Weibull-Geometrik, yaitu fungsi survivalnya. Distribusi yang dihasilkan yaitu distribusi Discrete Weibull Geometrik (DWG), memiliki bentuk fungsi hazard turun, naik, dan unimodal serta cukup baik dalam memodelkan data lifetime diskrit (count data). Diakhir skripsi ini, juga dibahas penggunaan distribusi DWG yang diilustrasikan pada data waktu hidup pasien lupus nephritis dalam waktu hari sehingga merupakan data diskrit. Kemudian, ditunjukkan bahwa distribusi DWG sesuai untuk memodelkan data waktu hidup pasien lupus nephritis.

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Lifetime data is data that contains the lifetime of an individual or a product that is measured from the beginning of the research time until an event occurs. One distribution that is often used for lifetime data analysis is Weibull distribution, because it has a constant, increasing, and decreasing hazard function. However, there is lifetime data with another form of the hazard function, that is the unimodal form (upside-down bathtub). Because of this, we developed Weibull distribution using the compounding method to produce a Weibull-Geometric distribution that can model lifetime data in unimodal hazard function form. But in fact, there are discrete lifetime data (count data). Hence, this paper discuss the formation of distributions that can model discrete lifetime data, which is obtained by discretizing a continuous Weibull-Geometric distribution (WG). Discretization is carried out by maintaining one of the characteristics of the Weibull-Geometric distribution, that is, its survival function. The result distribution, discrete Weibull Geometric distribution (DWG), has a form of increasing, decreasing, and unimodal hazard function, and quite good at modelling discrete lifetime data (count data). At the end of paper, the DWG distribution is used to illustrate dataset of lifetime patients lupus nephritis and shown that the DWG distribution is the appropriate model.

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