We present some properties of measures (<svg style="vertical-align:-2.29482pt;width:7.9124999px;" id="M2" height="9.875" version="1.1" viewBox="0 0 7.9124999 9.875" width="7.9124999"  xmlns="http://www.w3.org/2000/svg">
	<g transform="matrix(1.25,0,0,-1.25,0,9.875)">
		<g transform="translate(72,-64.1)">
			<text transform="matrix(1,0,0,-1,-71.95,66.44)">
				<tspan style="font-size: 12.50px; " x="0" y="0">𝑞</tspan>
			</text>

		</g>
	</g>
</svg>-Gaussian) that orthogonalize the set of <svg style="vertical-align:-2.29482pt;width:7.9124999px;" id="M3" height="9.875" version="1.1" viewBox="0 0 7.9124999 9.875" width="7.9124999"  xmlns="http://www.w3.org/2000/svg">
	<g transform="matrix(1.25,0,0,-1.25,0,9.875)">
		<g transform="translate(72,-64.1)">
			<text transform="matrix(1,0,0,-1,-71.95,66.44)">
				<tspan style="font-size: 12.50px; " x="0" y="0">𝑞</tspan>
			</text>

		</g>
	</g>
</svg>-Hermite polynomials. We also present an algorithm for simulating i.i.d. sequences of random variables having <svg style="vertical-align:-2.29482pt;width:7.9124999px;" id="M4" height="9.875" version="1.1" viewBox="0 0 7.9124999 9.875" width="7.9124999"  xmlns="http://www.w3.org/2000/svg">
	<g transform="matrix(1.25,0,0,-1.25,0,9.875)">
		<g transform="translate(72,-64.1)">
			<text transform="matrix(1,0,0,-1,-71.95,66.44)">
				<tspan style="font-size: 12.50px; " x="0" y="0">𝑞</tspan>
			</text>

		</g>
	</g>
</svg>-Gaussian distribution.

Pawe&#322; J. Szab&#322;owski

<svg style="vertical-align:-3.50804pt" height="12.1125" version="1.1" viewBox="0 0 8.4750004 12.1125" width="8.4750004" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path id="x1D45E" d="M474 429q-19 -69 -47 -222l-65 -347q-8 -49 0 -60t49 -16l26 -3l-4 -26l-246 -12l4 25l17 3q37 6 50 20.5t23 60.5l67 321h-2q-65 -79 -150 -138q-69 -47 -104 -47q-28 0 -48.5 32t-20.5 81q0 78 35 148t90 117q67 57 161 77q23 5 58 5q43 0 90 -15zM387 387&#xA;q-30 16 -75 16q-58 0 -92 -27q-49 -39 -78.5 -112t-29.5 -136q0 -34 8.5 -52.5t21.5 -18.5q40 0 109.5 63.5t103.5 115.5q16 53 32 151z" /></g></svg>-Gaussian Distributions: Simplifications and Simulations

The spurious regression phenomenon in least squares occurs for a wide range
of data generating processes, such as driftless unit roots, unit roots with drift,
long memory, trend and broken-trend stationarity. Indeed, spurious regressions
have played a fundamental role in the building of modern time series econometrics
and have revolutionized many of the procedures used in applied macroeconomics. Spin-offs from this research range from unit-root tests to cointegration and error-correction models. This paper provides an overview of results about spurious
regression, pulled from disperse sources, and explains their implications.

D. Ventosa-Santaul&#224;ria

Spurious Regression

It is well known that when (re)insurance coverages involve a deductible, the
impact of inflation of loss amounts is distorted, and the changes in claims paid by the
(re)insurer cannot be assumed to reflect the rate of inflation. A particularly interesting
phenomenon occurs when losses follow a Pareto distribution. In this case, the observed loss
amounts (those that exceed the deductible) are identically distributed from year to year
even in the presence of inflation. Nevertheless, in this paper we succeed in estimating the
inflation rate from the observations. We develop appropriate statistical inferential methods
to quantify the inflation rate and illustrate them using simulated data. Our solution hinges
on the recognition that the distribution of the number of observed losses changes from year
to year depending on the inflation rate.

Vytaras Brazauskas

Bruce L. Jones

Ri&#x10D;ardas Zitikis

When Inflation Causes No Increase in Claim Amounts

The paper studies the production inventory problem of minimizing
the expected discounted present value of production cost control in a manufacturing system with degenerate stochastic demand. We establish the existence of a
unique solution of the Hamilton-Jacobi-Bellman (HJB) equations associated with
this problem. The optimal control is given by a solution to the corresponding HJB
equation.

Azizul Baten

Anton Abdulbasah Kamil

Some Results on Bellman Equations of Optimal Production Control in a Stochastic Manufacturing System

We present a new method, based on the method of maximum entropy in the
mean, which builds upon the standard method of maximum entropy, to improve the parametric estimation of a decay rate when the measurements are corrupted by large level of
noise and, more importantly, when the number of measurements is small. The method is
developed in the context on a concrete example: that of estimation of the parameter in an
exponential distribution. We show how to obtain an estimator with the noise filtered out,
and using simulated data, we compare the performance of our method with the Bayesian
and maximum likelihood approaches.

Henryk Gzyl

Enrique Ter Horst

Recovering Decay Rates from Noisy Measurements with Maximum Entropy in the Mean

Current methods for mapping imprinted quantitative trait locus (iQTL) with inbred line
crosses assume fixed QTL effects. When an iQTL segregates in experimental line crosses,
combining different line crosses with similar genetic background can improve the accuracy
of iQTLs inference. In this article, we develop a general interval-based statistical variance
components framework to map iQTLs underlying complex traits by combining different
backcross line crosses. We propose a new iQTL variance partition method based on the
nature of marker alleles shared identical-by-decent (IBD) in inbred lines. Maternal effect is
adjusted when testing imprinting. Efficient estimation methods with the maximum likelihood
and the restricted maximum likelihood are derived and compared. Statistical properties of
the proposed mapping strategy are evaluated through extensive simulations under different
sampling designs. An extension to multiple QTL analysis is given. The proposed method
will greatly facilitate genetic dissection of imprinted complex traits in inbred line crosses.

Gengxin Li

Yuehua Cui

A Statistical Variance Components Framework for Mapping Imprinted Quantitative Trait Locus in Experimental Crosses

Discrete ancestral problems arising in population genetics are investigated.
In the neutral case, the duality concept has been proved of
particular interest in the understanding of backward in time ancestral process
from the forward in time branching population dynamics. We show that
duality formulae still are of great use when considering discrete nonneutral
Wright-Fisher models. This concerns a large class of nonneutral models with
completely monotone (CM) bias probabilities. We show that most classical
bias probabilities used in the genetics literature fall within this CM class or
are amenable to it through some &#8220;reciprocal mechanism&#8221; which we define.
Next, using elementary algebra on CM functions, some suggested novel evolutionary
mechanisms of potential interest are introduced and discussed.

Thierry E. Huillet

A Duality Approach to the Genealogies of Discrete Nonneutral Wright-Fisher Models

About this journal

<p><em>Journal of Probability and Statistics</em> publishes papers on the theory and application of probability and statistics that consider new methods and approaches to their implementation, or report significant results for the field.</p>


Journal profile

Meet the editorial board

<p><em>Journal of Probability and Statistics</em> maintains an Editorial Board of practicing researchers from around the world, to ensure manuscripts are handled by editors who are experts in the field of study.</p>


Editor spotlight

Submit your proposal

Do you think there is an emerging area of research that really needs to be highlighted? Or an existing research area that has been overlooked or would benefit from deeper investigation? Raise the profile of a research area by leading a Special Issue.

Special Issues

Author guidelines

Editorial board

Databases and indexing

Journal of Probability and Statistics - Table of contents

Journal of Probability and Statistics | Hindawi

title

Journal of Probability and Statistics publishes papers on the theory and application of probability and statistics that consider new methods and approaches to their implementation, or report significant results for the field.

Journal of Probability and Statistics