ANALISIS PEMILIHAN KARTU GSM PRABAYAR DI KALANGAN MAHASISWA DENGAN PENDEKATAN RANTAI MARKOV (Studi Kasus pada Mahasiswa Universitas Bunda Mulia, Jurusan Manajemen, Semester 8)

<p>The many variety of GSM card and services enables the customers to change brands easily. This has caused a tighter competition between the brands. In order to face the competition, GSM operators need to understand the customers’ perception and judgment on the preference scale toward the atribute of the products and services. GSM card operators also need to understand the brand switching pattern and its competitior position in analysing the market today or in the future. By the analyses, the operator hopes to acquired some description of their position and product situation among the tight competition between4 operators. The description can then be used as input in determining the marketing strategies for the future. The objects in this research are analyzed using Markov’s chain method on brand switching. The analysis on customer’s judgments on the product attributes and services is aided by the use of descriptive statistics. The case study is performed on the 8th semester students of Bunda Mulia University, majoring in Management. The population is 105 students. The research method is by using survey and the type of research is descriptive research. The data collecting technique is through the use of questionnaire and literary review. The results shows that the source of reference of the customer’s choice which is 3.81% from the event, 12.38% from families, 29.52 from commercials, 45.71% from friends, and 8.57% from other unspecified sources. The prediction of the market from the five operators in consequential orders are (0.0695, 0.6401, 0.0295, 0.1207, 0.1402), and the prediction of equilibrium moment are (0.0218, 0.5805, 0.0264, 0.117, 0.2543).The biggest market share is owned by XL which is 64.01%, and the smallest is by mentari with the share of 2.95%. The biggest sorce of reference for the students in choosing operators is from promotion events with the percentage of 30.81% and from friends is only 19.88%. Looking at this result it can be suggested that operators should increase their services and increase their promotion events in gaining the market share of GSM users.</p><p> </p><p>Keyword : GSM cards, brand switching, Markov’s chain, market share</p>

PENENTUAN KLASIFIKASI STATE PADA RANTAI MARKOV DENGAN MENGGUNAKAN NILAI EIGEN DARI MATRIKS PELUANG TRANSISI

Masalah dasar dari pemodelan stokastik dengan proses Markov adalah menentukan deskripsi state yang sesuai, sehingga proses stokastik yang berpadanan akan benar-benar memiliki sifat Markov, yaitu pengetahuan terhadap state saat ini adalah cukup untuk memprediksi perilaku stokastik dari proses di waktu yang akan datang. Penelitian ini dilakukan untuk menentukan klasifikasi state pada rantai Markov yang dibatasi untuk n = 4. Hasil penelitian ini menunjukkan bahwa untuk, state 4 terdapat satu state absorbing dan tiga state transient. Untuk batasan nilai terdapat dua state yang transient, dua state yang recurrent, dan membentuk satu kelas ekivalensi, sedangkan untuk batasan nilai terdapat dua state yang transient, dua state yang recurrent, dan termasuk state yang recurrent dalam satu kelas ekivalensi. DETERMINE CLASSIFICATION OF STATE IN MARKOV CHAIN USING EIGEN VALUE FROM TRANTITION PROBABILITY MATRIXABSTRACTBase problem from stochastic modal with Markov process is to determine appropriate state of description, in order that stochastic process corresponding will has truly Markov’s characteristic. Recently, it is adequate for knowledge of state to predict process of behavior stochastic in future. The research is intended to determine classification of state in Markov’s chain that is restriction to 4. The results indicate that for state,for 4. A restriction value will be formed one state transient, two states recurrent and one class of equivalent, while limited one will be formed two states transient, two states recurrent, and including one state recurrent inside one class of equivalent.

PROBABILIDADE DE OCORRÊNCIA DE PERÍODOS SECOS E CHUVOSOS EM PENTECOSTE, CE

PROBABILIDADE DE OCORRÊNCIA DE PERÍODOS SECOS E CHUVOSOS EM PENTECOSTE, CE Thales Vinícius de Araújo VianaBenito Moreira de AzevedoGuilherme Vieira do BomfimDepartamento de Engenharia Agrícola, Universidade Federal do Ceará, Fortaleza, CE. CEP60350-550. E-mail: [email protected]érson Soares de Andrade JúniorEmbrapa Meio Norte, Teresina, PI, CP, CEP 0164006-220. E-mail: [email protected] 1 RESUMO O objetivo deste trabalho foi determinar as probabilidades de ocorrência de períodos secos e chuvosos em Pentecoste, CE, a partir de uma série de 23 anos de dados diários de precipitação. Consideraram-se dias secos, os dias que apresentaram déficit hídrico, ou seja, os dias com precipitação nula ou inferior a evapotranspiração de referência. O estudo foi realizado para períodos decendiais, nos meses com precipitação média mensal superior a 60 mm (janeiro a maio). As probabilidades de ocorrência foram estimadas através da cadeia de Markov. A probabilidade de ocorrerem dias com déficit hídrico foi sempre superior a de dias chuvosos. As maiores probabilidades de ocorrerem dias com déficit hídrico foram registradas no primeiro e segundo decêndio de janeiro, primeiro de fevereiro e segundo e terceiro de maio. A maior probabilidade de ocorrência de dias chuvosos foi registrada no terceiro decêndio de março. A probabilidade de ocorrência de quatro dias consecutivos chuvosos foi muito baixa, sendo a maior no terceiro decêndio de fevereiro. UNITERMOS: precipitação, veranico, cadeia de Markov. VIANA, T. V. de A.; AZEVEDO, B. M. de; BOMFIM, G. V.; ANDRADE JÚNIOR, A. S. de A. PROBABILITY OF OCCURRENCE OF DRY AND RAINY SPELLS IN PENTECOSTE, CE. 2 ABSTRACT The objective of this work was to determine the probability of dry and rainy spell occurrence in Pentecoste, CE, using a 23 year-data historical series. The current study was accomplished for spells of ten days throughout those months with a monthly mean precipitation larger than 60 mm (January to May). The occurrence probabilities were estimated by means of Markov’s chain. The probability of occurrence of dry days was always superior to the rainy days. The largest probabilities of dry days were registered in the first and second ten day period of January, first ten day period of February and second and third ten day period of May. The largest probability of occurrence of rainy days was registered in the third ten day period of March. The occurrence probability of four rainy serial days was very low, with the largest value in the third ten day period of February. key words: rainfall, sequence of dry days, Markov’s chain.

Sets generated by stochastic automata of Markov’s chain type

In the earlier paper of the author [2] it has been introduced the concept of the generability for stochastic automaton. Here we give new necessary and sufficient conditions for the generability of the set of infinite sequences of automaton states. Moreover, we consider the generability of subset, complement, union, intersection and difference of generable sets.

On extension of stochastic k-automata

There are a great many research works concerning the well-known stochastic automata of Moore, Mealy, Rabin, Turing and others. Recently an automaton of Markov’s chain type has been introduced by Bartoszyński. This automaton is obtained by a generalization of Pawlak’s deterministic machine. The aim of this note is to give a concept of a stochastic automaton of Markov’s generalized chain type. The introduced automaton called a stochastic k-automaton (s.k-a.) is a common generalization of Bartoszyński’s automaton and Grodzki’s deterministic k-machine. By a stochastic k-automaton we mean an ordered triple M k = ⟨ U , a , π ⟩, k ⩾ 1, where U denotes a finite non-empty set, a is a function from Uk to [0, 1] with ∑ v ∈ U k a ( v ) = 1, and π is a function from Uk+1 to [0,1] with ∑ u ∈ U π ( v , u ) = 1 for every v ∈ U k . For all N ⩾ k we can define a probability measure PN on U N = U × U × … × U as follows: P N ( u 1 , u 2 , … , u N ) = a ( u 1 , u 2 , … , u k ) π ( u 1 , u 2 , … , u k + 1 ) π ( u 2 , u 3 , … , u k + 2 ) … π ( u N − k , u N − k + 1 , … , u N ). We deal with the problems of the shrinkage and the extension of a system of s.k-a.’s M k ( i ) = ⟨ U , a ( i ) , π ( i ) ⟩, i = 1 , 2 , … , m , m ⩾ 2. In this note there are given conditions under which an s.k-a. M k = ⟨ U , a , π ⟩ exists and the language of this automaton defined as L M = { ( u 1 , u 2 , u 3 , … ) : ∧ N ⩾ 1 P N ( u l , u 2 , … u N ) > 0 } either contains the languages of all the automata M k ( i ) , i = 1 , 2 , … , m, or this language equals the intersection of all those languages.