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: Pendugaan Fungsi Nilai Harapan pada Proses Poisson Periodik Majemuk dengan Tren Fungsi Pangkat
Abstrak: This manuscript is concerned with consistent estimation of the mean function of a compound cyclic Poisson process with power function trend. The cyclic component of intensity function of this process is not assumed to have any parametric form, but its period is assumed to be known. The slope of the power function trend is assumed to be positive, but its value is unknown. The main problems of this manuscript are constructing an estimator of this mean function, proving consistency of this estimator, and determining the rate of convergence to zero for the bias, variance, and mean squared error of this estimator, when the length of the observation time interval indefinitely expands.
Keyword: Bogor Agricultural University, the mean function., power function trend, cyclic intensity function, consistency, compound cyclic Poisson process

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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