Nearly fifty years after the introduction of skew Brownian motion by Itô and
McKean (1963), the first passage time distribution remains unknown. In this
paper, we first generalize results of Pitman and Yor (2001) and Csáki and Hu
(2004) to derive formulae for the distribution of ranked excursion heights of...
The "coupon collection problem" refers to a class of occupancy problems,
in which j identical items are distributed, independently and at random,
to n cells, with no restrictions on multiple occupancy. Identifying the cells as
coupons, a coupon is "collected" if the cell is occupied by one or more of...
This study was concerned with the estimation of transition probabilities
in a finite state Markov-type student flow model. Goals
setting for this study were three in number: (1) Study of the methods
which will provide conclusions that (a) the transition probabilities
are stationary or nonstationary and (b) the process is...
This thesis is concerned with the problem of developing a
method to categorize probability models by their outlier properties.
There have been two such categorization methods proposed in the
literature. Neyman and Scott (1971) classify an entire family of
distributions into the outlier properties outlier-prone completely
(OPC) and outlier resistant....
Before we apply the laws of probability to hiring practices, a
foundation of basic probability theory will be presented. In this
presentation a number of theorems related to probability will be
proven. These theorems are not necessarily applicable to the problem
which follows; however, they are basic to probability theory...
Methods of approximation and estimation of the density and the
cumulative distribution function of a distribution over a finite interval
are investigated. Goodness of the methods is measured pointwise and
in terms of mean integrated squared error (MISE).
If the density obeys certain regulatory conditions, i. e. , continuous,
A probability model has been developed for the survival of
irradiated bacteria with respect to the dose of radiation. This model
is applicable to those bacterial taxa to which the target theory applies.
Three estimation procedures are given for the purpose of
obtaining estimates of the probability model's parameters. These...