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FUNGSI KARAKTERISTIK DISTRIBUSI THREE-PARAMETER GENERALIZED RAYLEIGH
ABSTRAK Tujuan utama penelitian ini adalah menentukan fungsi karakteristik dari distribusi three-parameter generalized Rayleigh. Distribusi three-parameter generalized Rayleigh memiliki tiga parameter yaitu parameter bentuk ( ), parameter skala ( ) dan parameter lokasi ( ). Fungsi karakteristik dapat digunakan untuk menentukan fungsi distribusi dari suatu peubah acak yang dikenal sebagai teorema inversi fungsi karakteristik. Fungsi karakteristik dapat ditentukan dengan menggunakan definisi dan ekspansi trigonometri. Kedua cara tersebut bertujuan untuk menunjukkan kesamaan bentuk fungsi karakteristik dari distribusi three-parameter generalized Rayleigh yang diperoleh, kemudian dilanjutkan pembuktian sifat-sifat dasar fungsi karakteristik. Kata kunci : distribusi Rayleigh, distribusi generalized Rayleigh, distribusi three-parameter generalized Rayleigh, fungsi karakteristik, sifat-sifat dasar fungsi karakteristik. ABSTRACT The main purpose of this research is to derive the characteristic function of the three-parameter generalized Rayleigh distribution. The three-parameter generalized Rayleigh distribution has three parameter which are : the shape parameter ( ), the scale parameter ( ) and the location parameter (μ). The characteristic function can be used to determine the distribution function from a random variable that is known as inversion theorem of characteristic function. The characteristic function can be determined by using the definition and trigonometry expansion. Both methods show similiar form of the characteristic function of the three-parameter generalized Rayleigh distribution. This research also discusses the fundamental properties of the characteristic function of the three-parameter generalized Rayleigh distribution Keywords : Rayleigh distribution, generalized Rayleigh distribution, three-parameter generalized Rayleigh distribution, characteristics function, the properties of characteristic function.
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