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.
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.
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.
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.
Abstract: In this article, we consider the estimation of P[Y < X], when strength, X and stress, Y are two independent variables of Burr Type XII distribution. The MLE of the R based on one simple iterative procedure is obtained. Assuming that the common parameter is known, the maximum likelihood estimator, uniformly minimum variance unbiased estimator and Bayes estimator of P[Y < X] are discussed. The exact confidence interval of the R is also obtained. Monte Carlo simulations are performed to compare the different proposed methods.
Abstract: The log periodogram regression is widely used in empirical
applications because of its simplicity, since only a least squares
regression is required to estimate the memory parameter, d, its good
asymptotic properties and its robustness to misspecification of the
short term behavior of the series. However, the asymptotic distribution
is a poor approximation of the (unknown) finite sample distribution
if the sample size is small. Here the finite sample performance of different
nonparametric residual bootstrap procedures is analyzed when
applied to construct confidence intervals. In particular, in addition to
the basic residual bootstrap, the local and block bootstrap that might
adequately replicate the structure that may arise in the errors of the
regression are considered when the series shows weak dependence in
addition to the long memory component. Bias correcting bootstrap
to adjust the bias caused by that structure is also considered. Finally,
the performance of the bootstrap in log periodogram regression based
confidence intervals is assessed in different type of models and how
its performance changes as sample size increases.
Abstract: Using a set of confidence intervals, we develop a
common approach, to construct a fuzzy set as an estimator for
unknown parameters in statistical models. We investigate a method
to derive the explicit and unique membership function of such fuzzy
estimators. The proposed method has been used to derive the fuzzy
estimators of the parameters of a Normal distribution and some
functions of parameters of two Normal distributions, as well as the
parameters of the Exponential and Poisson distributions.
Abstract: Switched-mode converters play now a significant role in
modern society. Their operation are often crucial in various electrical
applications affecting the every day life. Therefore, the quality of
the converters needs to be reliably verified. Recent studies have
shown that the converters can be fully characterized by a set of
frequency responses which can be efficiently used to validate the
proper operation of the converters. Consequently, several methods
have been proposed to measure the frequency responses fast and
accurately. Most often correlation-based techniques have been applied.
The presented measurement methods are highly sensitive to
external errors and system nonlinearities. This fact has been often
forgotten and the necessary uncertainty analysis of the measured
responses has been neglected. This paper presents a simple approach
to analyze the noise and nonlinearities in the frequency-response
measurements of switched-mode converters. Coherence analysis is
applied to form a confidence interval characterizing the noise and
nonlinearities involved in the measurements. The presented method is
verified by practical measurements from a high-frequency switchedmode
converter.
Abstract: Given a bivariate normal sample of correlated variables,
(Xi, Yi), i = 1, . . . , n, an alternative estimator of Pearson’s correlation
coefficient is obtained in terms of the ranges, |Xi − Yi|.
An approximate confidence interval for ρX,Y is then derived, and
a simulation study reveals that the resulting coverage probabilities
are in close agreement with the set confidence levels. As well, a
new approximant is provided for the density function of R, the
sample correlation coefficient. A mixture involving the proposed
approximate density of R, denoted by hR(r), and a density function
determined from a known approximation due to R. A. Fisher is shown
to accurately approximate the distribution of R. Finally, nearly exact
density approximants are obtained on adjusting hR(r) by a 7th degree
polynomial.
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.
Abstract: In this paper, the estimation of the stress-strength
parameter R = P(Y < X), when X and Y are independent and both
are Lomax distributions with the common scale parameters but
different shape parameters is studied. The maximum likelihood
estimator of R is derived. Assuming that the common scale parameter
is known, the bayes estimator and exact confidence interval of R are
discussed. Simulation study to investigate performance of the
different proposed methods has been carried out.
Abstract: Zero inflated Strict Arcsine model is a newly developed model which is found to be appropriate in modeling overdispersed count data. In this study, maximum likelihood estimation method is used in estimating the parameters for zero inflated strict arcsine model. Bootstrapping is then employed to compute the confidence intervals for the estimated parameters.
Abstract: Oxidative stress is considered to be the cause for onset
and the progression of type 2 diabetes mellitus (T2DM) and
complications including neuropathy. It is a deleterious process that
can be an important mediator of damage to cell structures: protein,
lipids and DNA. Data suggest that in patients with diabetes and
diabetic neuropathy DNA repair is impaired, which prevents effective
removal of lesions. Objective: The aim of our study was to evaluate
the association of the hOGG1 (326 Ser/Cys) and XRCC1 (194
Arg/Trp, 399 Arg/Gln) gene polymorphisms whose protein is
involved in the BER pathway with DNA repair efficiency in patients
with diabetes type 2 and diabetic neuropathy compared to the healthy
subjects. Genotypes were determined by PCR-RFLP analysis in 385
subjects, including 117 with type 2 diabetes, 56 with diabetic
neuropathy and 212 with normal glucose metabolism. The
polymorphisms studied include codon 326 of hOGG1 and 194, 399
of XRCC1 in the base excision repair (BER) genes. Comet assay was
carried out using peripheral blood lymphocytes from the patients and
controls. This test enabled the evaluation of DNA damage in cells
exposed to hydrogen peroxide alone and in the combination with the
endonuclease III (Nth). The results of the analysis of polymorphism
were statistically examination by calculating the odds ratio (OR) and
their 95% confidence intervals (95% CI) using the ¤ç2-tests. Our data
indicate that patients with diabetes mellitus type 2 (including those
with neuropathy) had higher frequencies of the XRCC1 399Arg/Gln
polymorphism in homozygote (GG) (OR: 1.85 [95% CI: 1.07-3.22],
P=0.3) and also increased frequency of 399Gln (G) allele (OR: 1.38
[95% CI: 1.03-1.83], P=0.3). No relation to other polymorphisms
with increased risk of diabetes or diabetic neuropathy. In T2DM
patients complicated by neuropathy, there was less efficient repair of
oxidative DNA damage induced by hydrogen peroxide in both the
presence and absence of the Nth enzyme. The results of our study
suggest that the XRCC1 399 Arg/Gln polymorphism is a significant
risk factor of T2DM in Polish population. Obtained data suggest a
decreased efficiency of DNA repair in cells from patients with
diabetes and neuropathy may be associated with oxidative stress.
Additionally, patients with neuropathy are characterized by even
greater sensitivity to oxidative damage than patients with diabetes,
which suggests participation of free radicals in the pathogenesis of
neuropathy.
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.
Abstract: The aim of this study was to compare the effects
of an altitude training camp on heart rate variability and
performance in elite triathletes. Ten athletes completed 20 days of live-high, train-low training at 1650m. Athletes
underwent pre and post 800-m swim time trials at sea-level, and two heart rate variability tests at 1650m on the first and
last day of the training camp. Based on their time trial results,
athletes were divided into responders and non-responders. Relative to the non-responders, the responders sympathetic-toparasympathetic
ratio decreased substantially after 20 days of altitude training (-0.68 ± 1.08 and -1.2 ± 0.96, mean ± 90%
confidence interval for supine and standing respectively). In
addition, sympathetic activity while standing was also
substantially lower post-altitude in the responders compared to the non-responders (-1869 ± 4764 ms2). Results indicate that
responders demonstrated a change to more vagal
predominance compared to non-responders.
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.
Abstract: The double exponential model (DEM), or Laplace
distribution, is used in various disciplines. However, there are issues
related to the construction of confidence intervals (CI), when using
the distribution.In this paper, the properties of DEM are considered
with intention of constructing CI based on simulated data. The
analysis of pivotal equations for the models here in comparisons with
pivotal equations for normal distribution are performed, and the
results obtained from simulation data are presented.
Abstract: The present work analyses different parameters of pressure die casting to minimize the casting defects. Pressure diecasting is usually applied for casting of aluminium alloys. Good surface finish with required tolerances and dimensional accuracy can be achieved by optimization of controllable process parameters such as solidification time, molten temperature, filling time, injection pressure and plunger velocity. Moreover, by selection of optimum process parameters the pressure die casting defects such as porosity, insufficient spread of molten material, flash etc. are also minimized. Therefore, a pressure die casting component, carburetor housing of aluminium alloy (Al2Si2O5) has been considered. The effects of selected process parameters on casting defects and subsequent setting of parameters with the levels have been accomplished by Taguchi-s parameter design approach. The experiments have been performed as per the combination of levels of different process parameters suggested by L18 orthogonal array. Analyses of variance have been performed for mean and signal-to-noise ratio to estimate the percent contribution of different process parameters. Confidence interval has also been estimated for 95% consistency level and three conformational experiments have been performed to validate the optimum level of different parameters. Overall 2.352% reduction in defects has been observed with the help of suggested optimum process parameters.
Abstract: This paper evaluates the association between
economic environment in the districts of Madrid (Spain) and physical
inactivity, using income per capita as indicator of economic
environment. The analysis included 6,601 individuals aged 16 to 74
years. The measure of association estimated was the prevalence odds
ratio for physical inactivity by income per capita. After adjusting for
sex, age, and individual socioeconomic characteristics, people living
in the districts with the lowest per capita income had an odds ratio for
physical inactivity 1.58 times higher (95% confidence interval 1.35 to
1.85) than those living in districts with the highest per capita income.
Additional adjustment for the availability of sports facilities in each
district did not decrease the magnitude of the association. These
findings show that the widely believed assumption that the
availability of sports and recreational facilities, as a possible
explanation for the relation between economic environment and
physical inactivity, cannot be considered a universal observation.
Abstract: In this paper a stochastic scenario-based model predictive control applied to molten salt storage systems in concentrated solar tower power plant is presented. The main goal of this study is to build up a tool to analyze current and expected future resources for evaluating the weekly power to be advertised on electricity secondary market. This tool will allow plant operator to maximize profits while hedging the impact on the system of stochastic variables such as resources or sunlight shortage.
Solving the problem first requires a mixed logic dynamic modeling of the plant. The two stochastic variables, respectively the sunlight incoming energy and electricity demands from secondary market, are modeled by least square regression. Robustness is achieved by drawing a certain number of random variables realizations and applying the most restrictive one to the system. This scenario approach control technique provides the plant operator a confidence interval containing a given percentage of possible stochastic variable realizations in such a way that robust control is always achieved within its bounds. The results obtained from many trajectory simulations show the existence of a ‘’reliable’’ interval, which experimentally confirms the algorithm robustness.