Judul: Pendugaan Fungsi Nilai Harapan pada Proses Poisson Majemuk dengan Tren Linear
Abstrak: This manuscript is concerned with consistent estimation of the mean function of a compound cyclic Poisson process with linear trend. The cyclic component of intensity function of this process is not assumed to have any parametric form, but it period is assumed to be known. The slope of linear trend is assumed to be positif, but it value is unknown. The main problem of this manuscript are constructing an estimator of this mean function, proving consistency of this estimator, and proving that the bias, variance, and mean-squared error of this estimator converge to zero as the length of the observation time interval indefinitely expands.
Keyword: the mean function, linear trend, cyclic intensity function, consistency, Compound cyclic Poisson process

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: Kualitas Semen Cair Babi Dalam Pengencer Beltsville Thawing Solution Yang Ditambah Kuning Telur Dan Gliserol Disimpan Pada Suhu 5 °C Dan 18 °C
Abstrak: Penelitian ini bertujuan untuk membandingkan kualitas spermatozoa babi dalam pengencer beltsville thawing solution (BTS), BTS dicampur kuning telur dan BTS dicampur kuning telur dan gliserol yang disimpan pada suhu 5 °C dan 18 °C. Semen berasal dari 5 ekor babi jantan yang telah dewasa kelamin. Semen dievaluasi secara makroskopis dan mikroskopis segera setelah dikoleksi. Semen dibagi ke dalam 3 tabung dan masing-masing diencerkan dengan BTS, BTS dengan 20% kuning telur (BTS-KT) dan BTS dengan 15% kuning telur dan 5% gliserol (BTS-KTG). Setelah diencerkan, masing-masing tabung dibagi menjadi 2 tabung dan disimpan pada suhu 20-22 oC untuk holding time. Selanjutnya 3 tabung yang terdiri dari 3 pengencer yang berbeda disimpan pada suhu 5 °C dan 3 tabung lainnya disimpan pada 18 °C. Hasil penelitian menunjukkan pengencer terbaik untuk mempertahankan motilitas dan viabilitas spermatozoa adalah pengencer BTS-KT pada suhu 5 oC dan pengencer BTS pada suhu 18 °C. Kuning telur dapat melindungi spermatozoa babi dari cold shock pada suhu 5 oC. Gliserol tidak dapat digunakan untuk pembuatan semen cair karena gliserol tidak memberikan perubahan yang nyata pada kualitas semen cair.
Keyword: Babi jantan, BTS, gliserol, kuning telur, semen cair