Judul: Pendugaan Fungsi Nilai Harapan pada Proses Poisson Periodik Majemuk
Abstrak: A stochastic process has an important role in modeling various real phenomena. One special form of the stochastic process is a compound Poisson process. Many phenomena in different fields that have been modeled as a compound Poisson process, such as phenomena in the fields of insurance and finance, physics, demography, geology, and biology. A compound Poisson process model can be extended by generalizing the corresponding Poisson process. One of them is using cyclic Poisson process, so that the model becomes a compound cyclic Poisson process. This research has four objectives as follows: (1) to formulate an estimator of the mean function of a compound cyclic Poisson process; (2) to analyze the consistency of the estimator; (3) to analyze the bias, variance, and mean squared error (MSE) of the estimator; and (4) to observe the behavior of the estimator in the case that the length of the observation time interval is bounded. Let * ( ) + be a cyclic Poisson process with (unknown) locally integrable intensity function . We consider the case when the intensity function has a (known) period . We do not assume any (parametric) form of except that it is periodic, that is, the equality ( ) ( ) holds for all and . Let * ( ) + be a compound cyclic Poisson process that corresponds to the process * ( ) + where ( ) Σ ( ) with * + is a sequence of independent and identically distributed random variables having mean and variance , which is also independent of the process * ( ) +. The mean function of ( ) is given by ( ) , ( )- , ( )- , - . ( )/ where ⌊ ⌋ ( ) ∫ ( ) and ( ) Suppose that, for some , a single realization ( ) of the process * ( ) + defined on a probability space ( ) is observed, though only within a bounded interval , -. Furthermore, suppose that for each data point in the observed realization ( ) , -, say -th data point, 1, 2, , (, -), its corresponding random variable is also observed. The estimator of the mean function is given by ̂ ( ) . ̂ ̂ ( )/ ̂ where ̂ (, -) ̂ ( ) Σ (, - , -) and ̂ (, -)Σ (, -) with the understanding that ̂ when (, -) . The estimator of the mean function is both a weak and a strong consistent estimator, that is ̂ ( ) → ( ) and ̂ ( ) → ( ) as → . The rate of convergence of the bias, variance, and MSE of the estimator are respectively [ ̂ ( )] ( ) [ ̂ ( )] ( ) and [ ̂ ( )] ( ) as → . The behavior of the estimator is not good enough when the length of the time interval of observations is 20 period, but it is good enough when the length of the time interval of observations is 40
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Judul: Interval Kepercayaan untuk Fungsi Nilai Harapan dan Fungsi Ragam Proses Poisson Periodik Majemuk
Abstrak: Proses stokastik dapat digunakan untuk memprediksi atau menjelaskan kejadian-kejadian dalam kehidupan sehari-hari di masa mendatang. Salah satu bentuk dari proses stokastik adalah proses Poisson majemuk. Beberapa aplikasi proses Poisson majemuk di antaranya pada bidang fisika, demografi, seismologi, keuangan, asuransi, dan biologi. Pengembangan model proses Poisson majemuk dapat dilakukan dengan memperumum proses Poisson yang digunakan yaitu menggunakan proses Poisson periodik, sehingga modelnya menjadi proses Poisson periodik majemuk. Tujuan dari penelitian ini adalah: (i) merumuskan interval kepercayaan untuk fungsi nilai harapan dan fungsi ragam proses Poisson periodik majemuk, (ii) membuktikan kekonvergenan ke (1-α) peluang parameter tercakup pada interval kepercayaan, dengan α suatu taraf nyata, (iii) menentukan nilai n terkecil sehingga peluang parameter tercakup pada interval kepercayaan sudah mendekati 1-α, dengan simulasi komputer. ...dst, The stochastics process can be used to predict or explain events in everyday life in the future. One form of a stochastic process is the compound Poisson process. Some applications of the compound Poisson process are in physics, demography, seismology, finance, insurance, and biology. The development of a compound Poisson process model can be done by generalizing the Poisson process used by using the periodic Poisson process, so that the model becomes a compound periodic Poisson process. The objectives of this study are: (i) to formulate confidence intervals for the mean (expected value) and variance functions of compound cyclic Poisson process, (ii) to prove convergence to (1-α) for the probability that the parameters contained in the confidence interval, (iii) to determine the smallest n so that the probability that the parameters contained in the confidence intervals already close to 1-α, using computer simulation. ...dst
Keyword: mean function, variance function, periodic function, confidence interval, compound cyclic Poisson periodic

Judul: Penyakit transmissible gastroenteritas oleh virus corona pada babi
Abstrak: Trasnmissible Gastroenteritis pada babi oleh virus merupakan penyakit infeksius yang ditemukan pertama kali oleh Doyle dan Hutchings tahun 1946 di Indiana USA. Sehubungan dengan tingginya mortalitas akibat pe- nyakit TGE pada anak-anak babi serta kerugian yang beru- pa penurunan berat badan secara drastis pada babi yang dewasa, maka perlu kiranya penyakit ini diperhitungkan bagi suatu usaha peternakan. Walaupun di Indonesia be- lum dilaporkan kejadian penyakit tersebut, tetapi kita perlu waspada terhadap kemungkinan masuknya penyakit bersama dengan babi-babi import yang banyak dijumpai di- peternakan besar di Indonesia. ...
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