Narrow Results

The geometric process (GP) has been widely utilized as a stochastic monotone model in the fields of probability and statistics. However, its practical application is often limited by certain assumptions. To address this, [Wu (2018). Doubly geometric process and applications. Journal of the Operational Research Society, 69(1), 66–67] introduced the doubly geometric process (DGP) as an extension of the GP model, relaxing some of its assumptions. Due to its ability to overcome the limitations of the GP model, the DGP has gained significant popularity in recent times. This study focuses on the parameter estimation problem for the DGP when the distribution of the first interarrival time follows a lognormal distribution with parameters $\delta$ and $\tau$. We employ the maximum likelihood method to obtain estimates for both the model parameters and the distribution parameters. Additionally, we investigate the asymptotic joint distribution and statistical properties such as asymptotic unbiasedness and consistency of the estimators. Furthermore, we propose a novel test procedure to distinguish between the GP and DGP models. To assess the performance of the estimators and the proposed test procedure, we conduct a simulation study involving various sample sizes and parameter values. Finally, we present an application of the developed methods in fitting data from bladder cancer patients.

Nonnegative variables exist widely in the renewal processes such as queueing process, insurance process, and production process and play an important role in the practical application of related fields. As a powerful tool for modeling nonnegative variables, this paper gives a form of truncated normal uncertainty distribution, and gives the expressions or calculation formulas of its inverse uncertainty distribution, expected value, variance, and moments. In order to better apply the truncated normal uncertainty distribution to practice, this paper also studies the parameter estimation of the truncated normal uncertainty distribution based on the method of moments, the method of maximum likelihood and the method of least squares, and derives the rejection region of the corresponding hypothesis testing. Finally, this paper also illustrates the above results with two real data examples.

We give a list of equivalent conditions for reversibility of the adjoint of a unital Schwarz map, with respect to a set of quantum states. A large class of such conditions is given by preservation of distinguishability measures: F-divergences, L₁-distance, quantum Chernoff and Hoeffding distances. Here we summarize and extend the known results. Moreover, we prove a number of conditions in terms of the properties of a quantum Radon–Nikodym derivative and factorization of states in the given set. Finally, we show that reversibility is equivalent to preservation of a large class of quantum Fisher informations and χ²-divergences.

Many agents in the real world are reluctant to change their mind. Such an “inertial” behavior may affect the dynamics and cooperation of agents. Here we study the effect of “inertia” in the framework of Minority Game by requiring agents to choose their strategies via hypothesis testing. We find both numerically and semi-analytically that the presence of “inertial” agents greatly improves global cooperation of the system.

A novel system for verifying signatures on Persian handwritten bank checks is presented, in this paper. The presented system includes two main phases called: training and verification phases. At first, the system is trained using some genuine signatures provided by each customer in training phase. Then verifying the signatures on incoming checks is carried out in the verification phase. Feature extraction step is conducted based on a new approach that uses Multitresolution box-counting (MRBC) method for estimating the fractal dimension of signatures. Here, signature verification is modeled as testing hypothesis, and decision about acceptance or rejection of signatures on incoming checks is carried out using Kolmogorov–Smirnov test. The presented system has been tested on two databases: our new created database and NISDCC database which was used for ICDAR 2009 signature verification competition. Our database has 1000 genuine signatures provided by 100 participants and 200 skilled forgeries copied from genuine samples by five forgers. In total our database includes 1200 Persian signatures. Obtained results show promising performance of the presented system for its application on Persian banks.

In this paper, a new irregularity criterion based on fractal dimensions is introduced. In fact, this criterion (which is called ONH criterion) is the state space version of Higuchi fractal dimension, which can discriminate stochastic and deterministic time series from each other. To compute this criterion, we have exploited "the amount of state vectors fluctuations" in embedding space. By varying the reconstruction delay in embedding space, one can obtain a logarithmic diagram of overall changes corresponding to reconstructed state space versus delays. The slope of the linear region of this diagram could be considered as a new irregularity criterion. To discriminate random and deterministic time series, this criterion is adopted as a new statistic for hypothesis testing. Probability density function of this statistic under H₀ hypothesis is constructed and regarding to a certain confidence level, one can determine whether randomness is accepted or rejected.

Statistical process control charts are intended to assist operators in detecting process changes. If a process change does occur, the control chart should detect the change quickly. If the operator is provided with an estimate as to when the process changed, the search to find the special cause can be more easily facilitated. We investigate a process-monitoring tool for Poisson count data that quickly responds to process mean count rate changes regardless of the magnitude of the change, while supplying useful diagnostic information. A likelihood ratio approach was used to develop a control chart for a permanent step change in a Poisson process rate parameter. The average run length (ARL) performance of this chart is compared to that of several Poisson cumulative sum (CUSUM) control charts. Our performance results show that the proposed chart performs better than any one CUSUM chart over a wide range of potential shift magnitudes. The proposed chart also provides maximum likelihood estimates of the time and the magnitude of the process shift. These crucial change point diagnostics can greatly enhance the special cause investigation.

Most of the existing research in multi-state systems relies on point estimation for modeling and optimization. The assessment of uncertainty during design is essential, yet variability in system performance is commonly ignored. Unfortunately, unlimited testing which could provide these arbitrarily accurate estimates is not economical. This paper describes a statistical inference technique to quantify the uncertainties inherent in limited testing. The methodology enables estimation of joint confidence intervals for both system and component performance distributions and subsequently provides a hypothesis testing procedure to perform objective assessments. This builds on previous research which has only addressed confidence bounds for system reliability. Instead of dichotomizing systems into acceptable and unacceptable classes, our approach can handle the case when a system exhibits three or more distinct performance levels. Thus, the method does not place restrictions on the flexibility of the underlying multi-state system concept. The value of the approach is illustrated using a case study and several experiments. The results indicate that joint confidence intervals produced by this procedure are accurate for a range of common confidence levels and sample sizes. It is also demonstrated how hypothesis testing and uncertainty assessment may be used to objectively measure system readiness.

In this paper a new generalization of the Wilcoxon test is proposed for the comparative reliability evaluation of alternative engineering designs. Using Monte Carlo simulations the performance of the new test is assessed against the results provided by four other two-sample tests for censored reliability data, i.e., the Gehan-Wilcoxon, Peto-Prentice, Logrank and modified Kolmogorov-Smirnov tests. The results of the simulations suggest that the Wilcoxon alternatives based on weight functions that are reliability function estimates, such as the Peto-Prentice and the Bohoris-Wilcoxon, are the most preferable for routine use.

In this paper, we consider the self-normalized asymptotic properties of the parameter estimators in the fractional Ornstein–Uhlenbeck process. The deviation inequalities, Cramér-type moderate deviations and Berry–Esseen bounds are obtained. The main methods include the deviation inequalities and moderate deviations for multiple Wiener–Itô integrals [P. Major, Tail behavior of multiple integrals and U-statistics, Probab. Surv. 2 (2005) 448–505; On a multivariate version of Bernsteins inequality, Electron. J. Probab. 12 (2007) 966–988; M. Schulte and C. Thäle, Cumulants on Wiener chaos: Moderate deviations and the fourth moment theorem, J. Funct. Anal. 270 (2016) 2223–2248], as well as the Delta methods in large deviations [F. Q. Gao and X. Q. Zhao, Delta method in large deviations and moderate deviations for estimators, Ann. Statist. 39 (2011) 1211–1240]. For applications, we propose two test statistics which can be used to construct confidence intervals and rejection regions in the hypothesis testing for the drift coefficient. It is shown that the Type II errors tend to be zero exponential when using the proposed test statistics.

The model for reception of the concentration gradient of the Hedgehog morphogen has been developed. The mechanism of co-operation of the proteins Patched, Smoothened, and Hedgehog is theoretically analyzed in terms of different versions of interactions within this group of proteins. The parametric stability of the modeled system is considered.

Second-order stochastic dominance plays an important role in reliability and various branches of economics such as finance and decision-making under risk, and statistical testing for the stochastic dominance is often useful in practice. In this paper, we present a test of stochastic equality under the constraint of second-order stochastic dominance based on the theory of empirical processes. The asymptotic distribution of the test statistic is obtained, and a simple method to compute the critical value is derived. Simulation results and real data examples are presented to illustrate the proposed test method.

This paper examines the performance of a new probability model developed in terms of the surface area and velocity of an aero-structure, and presents some relevant statistical inferences. Several examples will compare the robustness of three kinds of point estimators developed for the lift coefficient. Four different types of confidence intervals for the lift coefficient are also developed, and it is shown that the shortest length confidence interval is an UMA confidence interval. Using the probability model, the correlation coefficient between lift and velocity, and the relevant regression slope are computed. The inferences and the results of this paper can be used particularly in the designing process of an aero-structure, especially when there is some uncertainty about its surface area; this provides some flexibilities for aerodynamicists in determining some of the unknown design characteristics.

Assuming a covariance structure with blocked compound symmetry, it was showed that unbiased estimators for the covariance matrices are optimal under normality. In this paper, we derive the asymptotic distribution of the correlation matrix using unbiased estimators and discuss its use in hypothesis testing. The accuracy of the result is investigated through numerical simulation and the method is applied to real data.

In this chapter, we will introduce the classical linear regression theory, including the classical model assumptions, the statistical properties of the Ordinary Least Squares (OLS) estimator, the t-test and the F-test, as well as the Generalized Least Squares (GLS) estimator and related statistical procedures. This chapter will serve as a starting point from which we will develop modern econometric theory.

This chapter provides a brief summary of the use of mathematical models and associated statistical analysis which have contributed to research on the pathogenesis of HIV infection and etiology. A review of some associated statistical methods is included with an example hypothesis testing using a mathematical model.

The mathematical foundations of statistics as a separate discipline were laid by Fisher, Neyman and Wald during the second quarter of the last century. Subsequent research in statistics and the courses taught in the universities are mostly based on the guidelines set by these pioneers. Statistics is used in some form or other in all areas of human endeavor from scientific research to optimum use of resources for social welfare, prediction and decision-making. However, there are controversies in statistics, especially in the choice of a model for data, use of prior probabilities and subject-matter judgments by experts. The same data analyzed by different consulting statisticians may lead to different conclusions.

What is the future of statistics in the present millennium dominated by information technology encompassing the whole of communications, interaction with intelligent systems, massive data bases, and complex information processing networks? The current statistical methodology based on simple probabilistic models developed for the analysis of small data sets appears to be inadequate to meet the needs of customers for quick on line processing of data and making the information available for practical use. Some methods are being put forward in the name of data mining for such purposes. A broad review of the current state of the art in statistics, its merits and demerits, and possible future developments will be presented.

The accuracy of existing methods for gradient-based image flow estimation suffers from low-quality derivative estimation, lack of systematic error analysis, and heuristic selection.

In this paper we present an image flow estimator using the facet model and covariance propagation. The facet model provides high-quality derivatives, image noise variance estimates, and the effect of prefiltering at the same time. We propagate the covariance of the image data to the image flow vector, yielding a covariance matrix with each vector. From the raw flow field, a χ² test selects the estimates statistically significant from zero. This selection scheme successfully suppresses false alarms and bad estimates with a low misdetection rate. We further incorporate a flow field smoothness constraint to achieve higher motion field consistency. Experiments on both synthetic and real data, and comparison with other techniques show that at a 10% misdetection rate, our approach has an average error vector magnitude that is 25% less than that of Lucas and Kanade and a false alarm rate less than half of theirs.

The following sections are included:

• THE ROLE OF STATISTICS IN BUSINESS AND ECONOMICS
  • TV Show Ratings
  • ABC GPA
  • One, Two, Three, “Fore!”
  • Health Benefits of Oat Bran
  • Fertilizer Choice and Plant Growth Rate

• DESCRIPTIVE VERSUS INFERENTIAL STATISTICS
  • Baseball Players’ Batting Averages
  • Monthly Unemployment Rates
  • Comparison of Male and Female Earnings
  • Returns on Stocks and Bonds
  • Pitfalls of Comparing the Earnings of Males and Females
  • Sampling Survey of Residents’ Voting Decision
  • Unemployment Rate
  • Quality Control Via Sampling Data
  • A Record Drop in Stock Prices

• DEDUCTIVE VERSUS INDUCTIVE ANALYSIS IN STATISTICS

• Summary

• Questions and Problems

The following sections are included:

• INTRODUCTION

• CONCEPTS AND ERRORS OF HYPOTHESIS TESTING
  • Concepts
  • Type I and Type II Errors

• HYPOTHESIS TEST CONSTRUCTION AND TESTING PROCEDURE
  • Two Types of Hypothes is Tests
  • The Trade-off Between Type I and Type II Errors
  • The P-Value Approach to Hypothesis Testing

• ONE-TAILED TESTS OF MEANS FOR LARGE SAMPLES
  • One-Sample Tests of Means
  • Two-Samples Tests of Means

• TWO-TAILED TESTS OF MEANS FOR LARGE SAMPLES
  • One-Sample Tests of Means
  • Confidence Intervals and Hypothesis Testing
  • Two-Samples Tests of Means

• SMALL-SAMPLE TESTS OF MEANS WITH UNKNOWN POPULATION STANDARD DEVIATIONS
  • One-Sample Tests of Means
  • Two-Samples Tests of Means

• HYPOTHESIS TESTING FOR A POPULATION PROPORTION
  • The Promotability of Company Employees
  • Defects in Canned Food

• CHI-SQUARE TESTS OF THE VARIANCE OF A NORMAL DISTRIBUTION
  • Variability in Customer Waiting Time

• COMPARING THE VARIANCES OF TWO NORMAL POPULATIONS

• BUSINESS APPLICATIONS
  • EPS and Rates of Return for GM Versus Those for Ford
  • Analysis of the Bank Risk Premium⁶
  • Analysis of Rates of Return for Retail Firms⁷
  • Hypothesis Testing Approach to Interpret the Quality Control Chart
  • Comparison of Organizational Values at Two Different Companies

• Summary

• Appendix 11A The Power of a Test, the Power Function, and the Operating-Characteristic Curve
  • The Power of a Test and the Power Function
  • Operating-Characteristic Curve⁹

• Questions and Problems