Fisher information in exponential-weighted location-scale distributions

In this article, the comparison between the Fisher information on parameters of the weighted distributions and the parent distributions is done. The most common family of distributions, location–scale family, is considered with the exponential weight function w(x) = e^βx where β is a constant. Conditions under which the weighted distributions are more (less) informative than the parent distribution are given. This was done for location, scale, and location–scale families when the scale parameter is considered as a nuisance parameter. Furthermore, using the transformation technique, we show that the results in location–scale family can be generalized to the broader classes of problems that studied the Fisher information of the weighted distributions such as Tzavelas and Economou (2014 Tzavelas, G., and P. Economou. 2014. Characterization properties based on the fisher information for weighted distributions. Statistics and Probability Letters 84:54–9.[Crossref], [Web of Science ®] , [Google Scholar]). As the exponential weight function can include some other weight functions, the obtained results in this article can be generalized for some other weight functions.     

On a Skew Bimodal Normal–Normal distribution fitted to the Old-Faithful geyser data

The Bimodal Normal distribution introduced by Alavi (2011) is a symmetric distribution where its variance is three times the variance of the corresponding normal distribution. Azzalini (1985) introduced the univariate Skew Normal distribution to model asymmetry data. In this paper the Skew Bimodal Normal–Normal distribution is introduced as a skew-symmetric distribution generated by the cumulative function of standard normal. Some properties of the distribution and some methods for generating data from this distribution are introduced. The maximum likelihood estimation of parameters is obtained. The distribution is fitted to the Old Faithful Geyser data.     

Form-invariance under weighted sampling

In this paper, form-invariant weighted distributions are considered in an exponential family. The class of bivariate distribution with invariant property is identified under exponential weight function. The class includes some of the custom bivariate models. The form-invariant multivariate normal distributions are obtained under a quadratic weight function.     

Quality of life and sexual function in postmenopausal women

This study examined the relationship between quality of life (QoL) and sexual function among postmenopausal women. As a cross-sectional study, it was conducted among 405 postmenopausal women selected using a multistage sampling method. The data-collection tools were the Female Sexual Function Index (FSFI) questionnaire, the WHO Quality of Life-BREF (WHOQOL-BREF) questionnaire, and a researcher-administered questionnaire. Sexual dysfunction was observed in 61% of the participants. The total scores of FSFI had a positive correlation with the WHOQOL-BREF total scores and all QoL domain scores. Therefore, sexual function needs to be covered by health-care packages aiming to improve postmenopausal women’s QoL.     

Robust surface estimation in multi-response multistage statistical optimization problems

As the ordinary least squares (OLS) method is very sensitive to outliers as well as to correlated responses, a robust coefficient estimation method is proposed in this paper for multi-response surfaces in multistage processes based on M-estimators. In this approach, experimental designs are used in which the intermediate response variables may act as covariates in the next stages. The performances of both the ordinary multivariate OLS and the proposed robust multi-response surface approach are analyzed and compared through extensive simulation experiments. Sum of the squared errors in estimating the regression coefficients reveals the efficiency of the proposed robust approach.     

Modified branching process for the reliability analysis of complex systems: Multiple-robot systems

Current design practice is usually to produce a safety system which meets a target level of performance that is deemed acceptable by the regulators. Safety systems are designed to prevent or alleviate the consequences of potentially hazardous events. In many modern industries the failure of such systems can lead to whole system breakdown. In reliability analysis of complex systems involving multiple components, it is assumed that the components have different failure rates with certain probabilities. This leads into extensive computational efforts involved in using the commonly employed generating function (GF) and the recursive algorithm to obtain reliability of systems consisting of a large number of components. Moreover, when the system failure results in fatalities it is desirable for the system to achieve an optimal rather than adequate level of performance given the limitations placed on available resources. This paper concerns with developing a modified branching process joint with generating function to handle reliability evaluation of a multi-robot complex system. The availability of the system is modeled to compute the failure probability of the whole system as a performance measure. The results help decision-makers in maintenance departments to analyze critical components of the system in different time periods to prevent system breakdowns.     

Aligning theory and methodology in mixed methods research: Before Design Theoretical Placement

When a theoretical framework (and its components) is not clearly linked to research methods, researchers risk designing flawed studies, wherein the stated research question is inconsistent with the research design. Explicitly identifying one’s theoretical orientation can provide an orderly schematic for linking observations from separate investigations (i.e. qualitative, quantitative) thereby facilitating understandings and guiding research designs particularly in fields of social and health sciences where complex phenomena are an aspect of the subject of inquiry. Although this has been established, how researchers might position their research theoretically to guide mixed methods research is less clear. In this paper, we propose the Before Design Theoretical Placement as a general guide for specifying and locating studies in a broader theoretical grounding, and discuss how it may inform overall study considerations. We then use this approach to illustrate how theories and methods can work together to facilitate professional knowledge development from a relational perspective.     

Statistical Monitoring of Autocorrelated Simple Linear Profiles Based on Principal Components Analysis

In this article, a transformation method using the principal component analysis approach is first applied to remove the existing autocorrelation within each profile in Phase I monitoring of autocorrelated simple linear profiles. This easy-to-use approach is independent of the autocorrelation coefficient. Moreover, since it is a model-free method, it can be used for Phase I monitoring procedures. Then, five control schemes are proposed to monitor the parameters of the profile with uncorrelated error terms. The performances of the proposed control charts are evaluated and are compared through simulation experiments based on different values of autocorrelation coefficient as well as different shift scenarios in the parameters of the profile in terms of probability of receiving an out-of-control signal.     

Economic design of VSI X̄ control chart with correlated non-normal data under multiple assignable causes

It has been recently revealed that the Shewhart control charts with variable sampling interval (VSI) perform better than the traditional Shewhart chart with the fixed sampling interval in detecting shifts in the process. In most of these research works, the normality and independency of the process data or measurements are assumed and that the process is subjected to only one assignable cause. While, in practice, these assumptions usually do not hold, some recent studies are focused on working with only one or two of these violations. In this paper, the situation in which the process data are correlated and follow a non-normal distribution and that there is multiplicity of assignable causes in the process is considered. For this case, a cost model for the economic design of the VSI X? control chart is developed, where the Burr distribution is employed to represent the non-normal distribution of the process data. To obtain the optimal values of the design parameters, a genetic algorithm is employed in which the response surface methodology is applied. A numerical example is presented to show the applicability and effectiveness of the proposed methodology. Sensitivity analysis is also carried out to evaluate the effects of cost and input parameters on the performance of the chart.