STATISTICAL PROPERTIES AND PERSISTENCE OF ENUMERATE DISCRETE RANDOM VARIABLES

• Main Author: WIDYASTUTI ARIF SUSILO (NIM : 20114040), AYU
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/25980
• Institution: Institut Teknologi Bandung

Enumerate discrete random variables can be following several possible conditions: the number of random variables may be deterministic or stochastic distributed; the random variables are summed may be (in)dependent each other and (not) identically distributed. In particular, pay attention to enumerate dependent discrete random variables on Markov chain with the case of deterministic and identical Bernoulli random variables are summed. Moreover, discussed about enumerate dependent discrete random variables on Markov chain with three states contain two absorbing states. With respect to absorbing state, pay attention to persistence on Markov chain. Persistent means that a state is lasting for along time or difficult to get rid of. Persistence and absorbing state have a relationship that aligns, so that defined the persistence index of each Markov chain process consequential. Furthermore, determined the correlation of two random variables are summed (enumeration of random variables). This thesis studied about statistical properties of enumerate discrete random variables. Other than that, studied too about relationship between correlation and persistence index of each Markov chain process consequential. <br /> <br /> The results obtained in this thesis is statistical properties of enumerate independent discrete random variables. Furthermore, from enumerate dependent discrete random variables on Markov chain with the case of deterministic derived both classical and recursive methods in order to obtain probability generating function. For Markov chain with two states derived detail of recursive probability generating function of Vallois-Tapiero method as follows and recursive of its first two moments. Meanwhile, for relationship between correlation and persistence index of each Markov chain process obtained greater persistence index effect the greater of correlation. Enumerate discrete random variables can be applied to represent the number of claims incurred in a given period.