**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**440

# Search results for: confidence interval

##### 440 Confidence Interval for the Inverse of a Normal Mean with a Known Coefficient of Variation

**Authors:**
Arunee Wongkha,
Suparat Niwitpong,
Sa-aat Niwitpong

**Abstract:**

In this paper, we propose two new confidence intervals for the inverse of a normal mean with a known coefficient of variation. One of new confidence intervals for the inverse of a normal mean with a known coefficient of variation is constructed based on the pivotal statistic Z where Z is a standard normal distribution and another confidence interval is constructed based on the generalized confidence interval, presented by Weerahandi. We examine the performance of these confidence intervals in terms of coverage probabilities and average lengths via Monte Carlo simulation.

**Keywords:**
The inverse of a normal mean,
confidence interval,
generalized confidence intervals,
known coefficient of variation.

##### 439 Approximate Confidence Interval for Effect Size Base on Bootstrap Resampling Method

**Authors:**
S. Phanyaem

**Abstract:**

**Keywords:**
Effect size,
confidence interval,
Bootstrap Method.

##### 438 Confidence Intervals for the Difference of Two Normal Population Variances

**Authors:**
Suparat Niwitpong

**Abstract:**

Motivated by the recent work of Herbert, Hayen, Macaskill and Walter [Interval estimation for the difference of two independent variances. Communications in Statistics, Simulation and Computation, 40: 744-758, 2011.], we investigate, in this paper, new confidence intervals for the difference between two normal population variances based on the generalized confidence interval of Weerahandi [Generalized Confidence Intervals. Journal of the American Statistical Association, 88(423): 899-905, 1993.] and the closed form method of variance estimation of Zou, Huo and Taleban [Simple confidence intervals for lognormal means and their differences with environmental applications. Environmetrics 20: 172-180, 2009]. Monte Carlo simulation results indicate that our proposed confidence intervals give a better coverage probability than that of the existing confidence interval. Also two new confidence intervals perform similarly based on their coverage probabilities and their average length widths.

**Keywords:**
Confidence interval,
generalized confidence interval,
the closed form method of variance estimation,
variance.

##### 437 On Simple Confidence Intervals for the Normal Mean with Known Coefficient of Variation

**Authors:**
Suparat Niwitpong,
Sa-aat Niwitpong

**Abstract:**

In this paper we proposed the new confidence interval for the normal population mean with known coefficient of variation. In practice, this situation occurs normally in environment and agriculture sciences where we know the standard deviation is proportional to the mean. As a result, the coefficient of variation of is known. We propose the new confidence interval based on the recent work of Khan [3] and this new confidence interval will compare with our previous work, see, e.g. Niwitpong [5]. We derive analytic expressions for the coverage probability and the expected length of each confidence interval. A numerical method will be used to assess the performance of these intervals based on their expected lengths.

**Keywords:**
confidence interval,
coverage probability,
expected length,
known coefficient of variation.

##### 436 Coverage Probability of Confidence Intervals for the Normal Mean and Variance with Restricted Parameter Space

**Authors:**
Sa-aat Niwitpong

**Abstract:**

Recent articles have addressed the problem to construct the confidence intervals for the mean of a normal distribution where the parameter space is restricted, see for example Wang [Confidence intervals for the mean of a normal distribution with restricted parameter space. Journal of Statistical Computation and Simulation, Vol. 78, No. 9, 2008, 829–841.], we derived, in this paper, analytic expressions of the coverage probability and the expected length of confidence interval for the normal mean when the whole parameter space is bounded. We also construct the confidence interval for the normal variance with restricted parameter for the first time and its coverage probability and expected length are also mathematically derived. As a result, one can use these criteria to assess the confidence interval for the normal mean and variance when the parameter space is restricted without the back up from simulation experiments.

**Keywords:**
Confidence interval,
coverage probability,
expected length,
restricted parameter space.

##### 435 Confidence Intervals for the Coefficients of Variation with Bounded Parameters

**Authors:**
Jeerapa Sappakitkamjorn,
Sa-aat Niwitpong

**Abstract:**

In many practical applications in various areas, such as engineering, science and social science, it is known that there exist bounds on the values of unknown parameters. For example, values of some measurements for controlling machines in an industrial process, weight or height of subjects, blood pressures of patients and retirement ages of public servants. When interval estimation is considered in a situation where the parameter to be estimated is bounded, it has been argued that the classical Neyman procedure for setting confidence intervals is unsatisfactory. This is due to the fact that the information regarding the restriction is simply ignored. It is, therefore, of significant interest to construct confidence intervals for the parameters that include the additional information on parameter values being bounded to enhance the accuracy of the interval estimation. Therefore in this paper, we propose a new confidence interval for the coefficient of variance where the population mean and standard deviation are bounded. The proposed interval is evaluated in terms of coverage probability and expected length via Monte Carlo simulation.

**Keywords:**
Bounded parameters,
coefficient of variation,
confidence interval,
Monte Carlo simulation.

##### 434 Confidence Intervals for the Normal Mean with Known Coefficient of Variation

**Authors:**
Suparat Niwitpong

**Abstract:**

In this paper we proposed two new confidence intervals for the normal population mean with known coefficient of variation. This situation occurs normally in environment and agriculture experiments where the scientist knows the coefficient of variation of their experiments. We propose two new confidence intervals for this problem based on the recent work of Searls [5] and the new method proposed in this paper for the first time. We derive analytic expressions for the coverage probability and the expected length of each confidence interval. Monte Carlo simulation will be used to assess the performance of these intervals based on their expected lengths.

**Keywords:**
confidence interval,
coverage probability,
expected length,
known coefficient of variation.

##### 433 Comparing Interval Estimators for Reliability in a Dependent Set-up

**Authors:**
Alessandro Barbiero

**Abstract:**

In this paper some procedures for building confidence intervals for the reliability in stress-strength models are discussed and empirically compared. The particular case of a bivariate normal setup is considered. The confidence intervals suggested are obtained employing approximations or asymptotic properties of maximum likelihood estimators. The coverage and the precision of these intervals are empirically checked through a simulation study. An application to real paired data is also provided.

**Keywords:**
Approximate estimators,
asymptotic theory,
confidence interval,
Monte Carlo simulations,
stress-strength,
variance estimation.

##### 432 An Enhanced Floor Estimation Algorithm for Indoor Wireless Localization Systems Using Confidence Interval Approach

**Authors:**
Kriangkrai Maneerat,
Chutima Prommak

**Abstract:**

Indoor wireless localization systems have played an important role to enhance context-aware services. Determining the position of mobile objects in complex indoor environments, such as those in multi-floor buildings, is very challenging problems. This paper presents an effective floor estimation algorithm, which can accurately determine the floor where mobile objects located. The proposed algorithm is based on the confidence interval of the summation of online Received Signal Strength (RSS) obtained from the IEEE 802.15.4 Wireless Sensor Networks (WSN).We compare the performance of the proposed algorithm with those of other floor estimation algorithms in literature by conducting a real implementation of WSN in our facility. The experimental results and analysis showed that the proposed floor estimation algorithm outperformed the other algorithms and provided highest percentage of floor accuracy up to 100% with 95-percent confidence interval.

**Keywords:**
Floor estimation algorithm,
floor determination,
multi-floor building,
indoor wireless systems.

##### 431 On Some Properties of Interval Matrices

**Authors:**
K. Ganesan

**Abstract:**

**Keywords:**
Interval arithmetic,
Interval matrix,
linear equations.

##### 430 Comparison of Two Interval Models for Interval-Valued Differential Evolution

**Authors:**
Hidehiko Okada

**Abstract:**

The author previously proposed an extension of differential evolution. The proposed method extends the processes of DE to handle interval numbers as genotype values so that DE can be applied to interval-valued optimization problems. The interval DE can employ either of two interval models, the lower and upper model or the center and width model, for specifying genotype values. Ability of the interval DE in searching for solutions may depend on the model. In this paper, the author compares the two models to investigate which model contributes better for the interval DE to find better solutions. Application of the interval DE is evolutionary training of interval-valued neural networks. A result of preliminary study indicates that the CW model is better than the LU model: the interval DE with the CW model could evolve better neural networks.

**Keywords:**
Evolutionary algorithms,
differential evolution,
neural network,
neuroevolution,
interval arithmetic.

##### 429 Forecast of the Small Wind Turbines Sales with Replacement Purchases and with or without Account of Price Changes

**Authors:**
V. Churkin,
M. Lopatin

**Abstract:**

**Keywords:**
Bass model,
generalized Bass model,
replacement
purchases,
sales forecasting of innovations,
statistics of sales of small
wind turbines in the United States.

##### 428 Reliability Analysis of k-out-of-n : G System Using Triangular Intuitionistic Fuzzy Numbers

**Authors:**
Tanuj Kumar,
Rakesh Kumar Bajaj

**Abstract:**

In the present paper, we analyze the vague reliability of k-out-of-n : G system (particularly, series and parallel system) with independent and non-identically distributed components, where the reliability of the components are unknown. The reliability of each component has been estimated using statistical confidence interval approach. Then we converted these statistical confidence interval into triangular intuitionistic fuzzy numbers. Based on these triangular intuitionistic fuzzy numbers, the reliability of the k-out-of-n : G system has been calculated. Further, in order to implement the proposed methodology and to analyze the results of k-out-of-n : G system, a numerical example has been provided.

**Keywords:**
Vague set,
vague reliability,
triangular intuitionistic fuzzy number,
k-out-of-n : G system,
series and parallel system.

##### 427 The Reproducibility and Repeatability of Modified Likelihood Ratio for Forensics Handwriting Examination

**Authors:**
O. Abiodun Adeyinka,
B. Adeyemo Adesesan

**Abstract:**

**Keywords:**
Logistic Regression LoR,
Kernel Density Estimator KDE,
Handwriting,
Confidence Interval,
Repeatability,
Reproducibility.

##### 426 Approximations to the Distribution of the Sample Correlation Coefficient

**Authors:**
John N. Haddad,
Serge B. Provost

**Abstract:**

**Keywords:**
Sample correlation coefficient,
density approximation,
confidence intervals.

##### 425 Computational Aspects of Regression Analysis of Interval Data

**Authors:**
Michal Cerny

**Abstract:**

We consider linear regression models where both input data (the values of independent variables) and output data (the observations of the dependent variable) are interval-censored. We introduce a possibilistic generalization of the least squares estimator, so called OLS-set for the interval model. This set captures the impact of the loss of information on the OLS estimator caused by interval censoring and provides a tool for quantification of this effect. We study complexity-theoretic properties of the OLS-set. We also deal with restricted versions of the general interval linear regression model, in particular the crisp input – interval output model. We give an argument that natural descriptions of the OLS-set in the crisp input – interval output cannot be computed in polynomial time. Then we derive easily computable approximations for the OLS-set which can be used instead of the exact description. We illustrate the approach by an example.

**Keywords:**
Linear regression,
interval-censored data,
computational complexity.

##### 424 The Diameter of an Interval Graph is Twice of its Radius

**Authors:**
Tarasankar Pramanik,
Sukumar Mondal,
Madhumangal Pal

**Abstract:**

In an interval graph G = (V,E) the distance between two vertices u, v is de£ned as the smallest number of edges in a path joining u and v. The eccentricity of a vertex v is the maximum among distances from all other vertices of V . The diameter (δ) and radius (ρ) of the graph G is respectively the maximum and minimum among all the eccentricities of G. The center of the graph G is the set C(G) of vertices with eccentricity ρ. In this context our aim is to establish the relation ρ = δ 2 for an interval graph and to determine the center of it.

**Keywords:**
Interval graph,
interval tree,
radius,
center.

##### 423 Fuzzy Estimation of Parameters in Statistical Models

**Authors:**
A. Falsafain,
S. M. Taheri,
M. Mashinchi

**Abstract:**

**Keywords:**
Confidence interval. Fuzzy number. Fuzzy estimation.

##### 422 Computing Maximum Uniquely Restricted Matchings in Restricted Interval Graphs

**Authors:**
Swapnil Gupta,
C. Pandu Rangan

**Abstract:**

**Keywords:**
Uniquely restricted matching,
interval graph,
design
and analysis of algorithms,
matching,
induced matching,
witness
counting.

##### 421 Small Sample Bootstrap Confidence Intervals for Long-Memory Parameter

**Authors:**
Josu Arteche,
Jesus Orbe

**Abstract:**

**Keywords:**
bootstrap,
confidence interval,
log periodogram regression,
long memory.

##### 420 Particle Swarm Optimization with Interval-valued Genotypes and Its Application to Neuroevolution

**Authors:**
Hidehiko Okada

**Abstract:**

The author proposes an extension of particle swarm optimization (PSO) for solving interval-valued optimization problems and applies the extended PSO to evolutionary training of neural networks (NNs) with interval weights. In the proposed PSO, values in the genotypes are not real numbers but intervals. Experimental results show that interval-valued NNs trained by the proposed method could well approximate hidden target functions despite the fact that no training data was explicitly provided.

**Keywords:**
Evolutionary algorithms,
swarm intelligence,
particle swarm optimization,
neural network,
interval arithmetic.

##### 419 A Fuzzy Nonlinear Regression Model for Interval Type-2 Fuzzy Sets

**Authors:**
O. Poleshchuk,
E.Komarov

**Abstract:**

This paper presents a regression model for interval type-2 fuzzy sets based on the least squares estimation technique. Unknown coefficients are assumed to be triangular fuzzy numbers. The basic idea is to determine aggregation intervals for type-1 fuzzy sets, membership functions of whose are low membership function and upper membership function of interval type-2 fuzzy set. These aggregation intervals were called weighted intervals. Low and upper membership functions of input and output interval type-2 fuzzy sets for developed regression models are considered as piecewise linear functions.

**Keywords:**
Interval type-2 fuzzy sets,
fuzzy regression,
weighted interval.

##### 418 Lithofacies Classification from Well Log Data Using Neural Networks, Interval Neutrosophic Sets and Quantification of Uncertainty

**Authors:**
Pawalai Kraipeerapun,
Chun Che Fung,
Kok Wai Wong

**Abstract:**

This paper proposes a novel approach to the question of lithofacies classification based on an assessment of the uncertainty in the classification results. The proposed approach has multiple neural networks (NN), and interval neutrosophic sets (INS) are used to classify the input well log data into outputs of multiple classes of lithofacies. A pair of n-class neural networks are used to predict n-degree of truth memberships and n-degree of false memberships. Indeterminacy memberships or uncertainties in the predictions are estimated using a multidimensional interpolation method. These three memberships form the INS used to support the confidence in results of multiclass classification. Based on the experimental data, our approach improves the classification performance as compared to an existing technique applied only to the truth membership. In addition, our approach has the capability to provide a measure of uncertainty in the problem of multiclass classification.

**Keywords:**
Multiclass classification,
feed-forward backpropagation
neural network,
interval neutrosophic sets,
uncertainty.

##### 417 An Interval-Based Multi-Attribute Decision Making Approach for Electric Utility Resource Planning

**Authors:**
M. Sedighizadeh,
A. Rezazadeh

**Abstract:**

**Keywords:**
Decision Making,
Power Generation,
ElectricUtilities,
Resource Planning.

##### 416 Maximum Likelihood Estimation of Burr Type V Distribution under Left Censored Samples

**Abstract:**

The paper deals with the maximum likelihood estimation of the parameters of the Burr type V distribution based on left censored samples. The maximum likelihood estimators (MLE) of the parameters have been derived and the Fisher information matrix for the parameters of the said distribution has been obtained explicitly. The confidence intervals for the parameters have also been discussed. A simulation study has been conducted to investigate the performance of the point and interval estimates.

**Keywords:**
Fisher information matrix,
confidence intervals,
censoring.

##### 415 Solution of Interval-valued Manufacturing Inventory Models With Shortages

**Authors:**
Susovan Chakrabortty,
Madhumangal Pal,
Prasun Kumar Nayak

**Abstract:**

**Keywords:**
EOQ,
Inventory,
Interval Number,
Demand,
Production,
Simulation

##### 414 Some Results on Interval-Valued Fuzzy BG-Algebras

**Authors:**
Arsham Borumand Saeid

**Abstract:**

In this note the notion of interval-valued fuzzy BG-algebras (briefly, i-v fuzzy BG-algebras), the level and strong level BG-subalgebra is introduced. Then we state and prove some theorems which determine the relationship between these notions and BG-subalgebras. The images and inverse images of i-v fuzzy BG-subalgebras are defined, and how the homomorphic images and inverse images of i-v fuzzy BG-subalgebra becomes i-v fuzzy BG-algebras are studied.

**Keywords:**
BG-algebra,
fuzzy BG-subalgebra,
interval-valued fuzzy set,
interval-valued fuzzy BG-subalgebra.

##### 413 Ranking DMUs by Ideal PPS in Data Envelopment Analysis

**Authors:**
V.Rezaie,
M.Khanmohammady

**Abstract:**

**Keywords:**
Data envelopment analysis (DEA),
Decision makingunit (DMU),
Interval DEA,
Ideal points,
Ideal PPS,
Return to scale(RTS).

##### 412 Classifying and Predicting Efficiencies Using Interval DEA Grid Setting

**Authors:**
Yiannis G. Smirlis

**Abstract:**

**Keywords:**
Data envelopment analysis,
interval DEA,
efficiency classification,
efficiency prediction.

##### 411 Digital Redesign of Interval Systems via Particle Swarm Optimization

**Authors:**
Chen-Chien Hsu,
Chun-Hui Gao

**Abstract:**

**Keywords:**
Digital redesign,
Extremal systems,
Particle swarm optimization,
Uncertain interval systems