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,
positive,...
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...
Genetic markers from Bacteroides and other faecal bacteria are being tested for inclusion in regulations to quantify aquatic faecal contamination and estimate public health risk. For the method to be used quantitatively across environments, persistence and decay of markers must be understood. We measured concentrations of contaminant molecular markers targeting...
The exponential family of probability distributions is obtained
from σ-finite measures on the real line. We choose the parameter
space to be one-dimensional and the exponent to be linear. Relationships
between the measure, its spectrum, and the parameter space
are examined, moments of the exponential family are studied, and
the...
Gene regulation is a complex mechanism that controls the spatial and temporal expression of genes in a living cell. My dissertation studies focus on two problems. First, tissue-specific gene expression prediction from DNA sequence and chromatin state, and second, the accurate discovery of small over-represented regulatory circuits in gene regulatory...
This thesis gives a procedure for generalizing the concept of
conditional probability applied to the case of the bivariate probability
density function.
The conditional probability density function is desired where the two variables vary according to some prescribed path Φ which lies in the plane of the two variables. Instead...
This thesis discusses the design and evaluation of an instrument that can estimate the probability density distributions of bandlimited, aperiodic electrical phenomena. This estimator can obtain the probability density estimates of signals that are contained within the frequency range of 100 cps. to 20 kcs. However, the basic design logic...
Some nonparametric maximum likelihood estimation procedures
are developed for the class of pairs of distributions which have proportional
failure rate functions. Special consideration is given to the
case in which the shape of the failure rate functions are assumed to
be either increasing or decreasing. Estimators of the proportionality
constant,...