Generalized multivariate beta distribution : control charting when the measurements are from an exponential distribution

In Statistical Process Control (SPC) there exists a need to model the runlength distribution of a Q-chart that monitors the process mean when measurements are from an exponential distribution with an unknown parameter. To develop exact expressions for the probabilities of run-lengths the joint distribution of the charting statistics is needed. This gives rise to a new distribution that can be regarded as a generalized multivariate beta distribution. An overview of the problem statement as identified in the field of SPC is given and the newly developed generalized multivariate beta distribution is proposed. Statistical properties of this distribution are studied and the effect of the parameters of this generalized multivariate beta distribution on the correlation between two variables is also discussed.The National Research Foundation, South Africa (Grant: FA2007043000003 and the Thuthuka programme: TTK20100707000011868).http://www.springerlink.com/content/0932-5026/nf201

Body shape versus body form : a comparison of the body shapes of female Swazi consumers with those of body forms used in apparel manufacturing

Om goeie pas te verseker is dit belangrik dat klein- en grootskaalse klerevervaardigers klere vervaardig wat die groottes en liggaamsvorme van hul teikenmark sal pas. Vir die pas van klere maak groot- en kleinskaalse klerevervaar-digers gebruik van kommersiële pas-modelle, waarvan die groottes en vorme veronderstel is om dieselfde te wees as die groottes en vorme van die teikenmark. Soos in baie ander lande, is geen antropometriese data van die Swazi-populasie beskikbaar nie, en ondervind veral die kleinskaalse klerevervaardigers in Swazi-land steeds menige probleme met die pas van hul vervaardigde klere. Die doel van die studie was eerstens om die mees algemene vroulike Swazi-liggaamsvorm wat vir die vervaardiging van kommersiële pas-modelle gebruik kan word, te identifiseer, en tweedens om die mees algemene Swazi-liggaamsvorm met die lig-gaamsvorme van beskikbare kommersiële pas-modelle te vergelyk. Die steekproef het bestaan uit 101 jong Swazi-vroue, ouderdom 18-30 jaar, en met ’n grootte 32 en 34 borsmaat. Die studie is in twee fases uitgevoer. In fase 1 is die liggaamsmates van die steekproef en twee verskillende handels-naam kommersiële pas-modelle geneem en vergelyk. In fase 2 is die pas van ’n basiese rok wat volgens die mates van die geïdentifiseerde mees algemene Swazi-liggaamsvorm (grootte 32 en 34) gemaak is, op die kommersiële pas-modelle geëvalueer. Die resultate het getoon dat die mees algemene Swazi-liggaamsvorm die driehoekige liggaams-vorm is, gevolg deur die uurglas-liggaamsvorm. In teenstelling met wat verwag is, was die liggaamsvorm van die pas-modelle nie die uur-glas of ideale liggaamsvorm nie, maar wel ’n langwerpige en driehoekige liggaamsvorm. Daar was betekenisvolle verskille tussen die lig-gaamsmates van beide groottes driehoekige Swazi-liggaamsvorms en die mates van die twee verskillende handelsnaam-pas-modelle. Die evaluering van die pas van ’n basiese rok, gemaak volgens die mates van die geïden-tifiseerde mees algemene Swazi-liggaamsvorm (grootte 32 en 34 Swazi) op die kommersiële pas-modelle, het dan ook pas-probleme uitge-wys. Die resultate het implikasie vir vervaar-digers van pas-modelle sowel as van klere wat vir die Swazi-mark bedoel ishttp://reference.sabinet.co.za/sa_epublication/famecsam201

The role of important values and predominant identity in the dress practices of female Muslim students attending a South African university

This study explores the role of important values and predominant identity in the dress practices of female Muslim students attending a university in South Africa. Data were collected through a selfadministered questionnaire using a purposive convenience sample of 200 female Muslim students. A cluster analysis was used to divide participants into groups based on their dress practices. The sample could be divided into two groups: those who follow less modest and those who follow more modest dress practices. An independent t-test was calculated to determine if there was a significant difference between the important values and predominant identity of the less modest and more modest groups. The results revealed differences in the significance of certain values and predominant identity. The more modest group placed more importance on religious values, while the less modest group attributed more importance to social values than the more modest group. For the more modest group their Muslim identity was more predominant than for the less modest group. Despite these differences, both groups tended to communicate a hybrid identity, as aspects of Islamic and Western thought and behavior were synthesized in each individual’s dress practice. The study offers benefits to scholars interested in the social-cultural aspects of clothing by showing how people manipulate their appearances and cultural forms to create a specific reality and to adapt to multicultural environments (e.g. campuses).http://ctr.sagepub.comhb2016Consumer ScienceStatistic

Female Muslim students' dress practices in a South African campus context

Suid-Afrikaanse vroulike Muslim-studente volg 'n verskeidenheid van kleding-praktyke. Terwyl party individue baie tradisionele Islamietiese drag dra, volg ander Westerse modes. Hierdie verskille in klere kan aan die akkulturasieproses toegeskryf word. Die kampusomgewing het 'n multi-kulturele konteks. Vroulike Muslim-studente word omring deur nuwe waardes, identiteite en nuwe kledingpraktyke. Die doel van die studie was om die akkulturasie strategieë wat deur vroulike Muslim-studente (wat aan die Universiteit van Pretoria studeer) toegepas word in hul kledinggebruike te verken en te beskryf. 'n Kulturele perspektief is as teoretiese raamwerk gebruik. Die navorsingsontwerp was 'n verkennende ondersoek. Data is met 'n gestruktureerde vraelys ingesamel. Die vraelys is gebaseer op bestaande skale en relevante literatuur om die akkulturasie praktyke van vroulike Muslim-studente aan die hand van hul kledingpraktyke te analiseer. Die akkulturasie praktyke is deur middel van 'n 5-punt Likert-tipe skaal gemeet en 'n „prent‟ skaal is met die samewerking van 'n senior Muslim-student in die Departement Verbruikerswetenskap ontwikkel. Hierdie skaal het nege beelde van klere ingesluit wat verskil het in terme van pas en mate waartoe die liggaam bedek word. Die teikenpopulasie was ingeskrewe vroulike Muslim-studente aan die Universiteit van Pretoria. In 2011 was daar 354 vroulike Muslim studente ingeskryf by die Universiteit van Pretoria. 'n Totaal van 200 voltooide vraelyste wat deur vroulike Muslim-studente tussen die ouderdomme van 17 en 25 jaar voltooi is, is geanaliseer (n=200). Die oorkoepelende doel van hierdie studie was om die verskillende akkulturasie strategieë wat deur vroulike Muslim-studente se kledingprak-tyke gereflekteer word, te ondersoek en te beskryf. Die resultate het daarop gedui dat die respondente nie in drie groepe verdeel kon word na aanleiding van die akkulturasie strategieë wat hulle volg soos aanvanklik verwag is nie. Die respondente kon wel in twee groepe verdeel word, namens dié wat minder kuise kledingpraktyke volg teenoor dié met meer kuise, tradisionele kledingpraktyke. Die studie het aangetoon dat vroulike Muslim-studente verskillende grade van ‟n bi-kulturele identiteit aanvaar. Hierdie studie maak ‟n bydrae tot kulturele navorsing en kledingge-dragnavorsing in Suid-Afrika. Die feit dat die respondente slegs in twee groepe verdeel kon word op grond van die akkulturasie praktyke wat hulle toepas, dui daarop dat die respon-dente in hierdie studie onwillig is om Muslim herkoms, en gevolglik hul tradisionele klere-drag, te negeer. Hulle verkies om in wissel-werking te tree met ander kultuurgroepe soos tipies van 'n Suid-Afrikaanse universiteits-kampus, en kombineer hul tradisionele drag met elemente van Westerse drag om hul bi-kulturele identiteit te kommunikeer. Sodoende verbeeld hulle beide hul Muslim en Suid-Afrikaanse identiteite.http://www.up.ac.za/saafecsam201

Noncentral generalized multivariate Beta Type II distribution

The distribution of the variables that originates from monitoring the variance when the mean encountered a sustained shift is considered — specifically for the case when measurements from each sample are independent and identically distributed normal random variables. It is shown that the solution to this problem involves a sequence of dependent random variables that are constructed from independent noncentral chi- squared random variables. This sequence of dependent random variables are the key to understanding the performance of the process used to monitor the variance and are the focus of this article. For simplicity, the marginal (i.e. the univariate and bivariate) distributions and the joint (i.e. the trivariate) distribution of only the first three random variables following a change in the variance is considered. A multivariate generalization is proposed which can be used to calculate the entire run-length (i.e. the waiting time until the first signal) distribution.The National Research Foundation, South Africa (Grant: FA2007043000003 and the Thuthuka programme : TTK20100707000011868)http://www.ine.pt/revstat/inicio.htmlam201

Ethnicity, body shape differences and female consumers' apparel fit problems

This research compared body shapes, measurements, ratios and fit problems of 234 African (109) and Caucasian (125) women. A 3-dimensional (3D) full body scanner generated virtual body images from which circumferential, width, protrusion and height measurements were extracted. Thereafter, circumferential and height ratios were computed. Drop values of key circumferential measurements were used to classify participants’ bodies; these were later visually confirmed and adopted. Results revealed that the triangle, hourglass and rectangle were the three most predominant shapes amongst African and Caucasian women. There was a significant association between the three most predominant body shapes and ethnicity. There were significant differences in some body measurements and ratios, most of which were observed between African and Caucasian triangle shapes, as well as in some of the other body shapes and the Caucasian hourglass used in the apparel industry. The differences especially between the Caucasian hourglass and the other body shapes may be the root cause of the persistent fit problems reported by some of the predominant body shapes at some of the selected body parts. This study therefore, concluded that multi-cultural markets need to identify characteristics of all prevalent shapes within a population in order to minimise apparel fit problems.http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1470-6431hb201

Generalised beta type II distributions - emanating from a sequential process

This study focuses on the development of a generalised multivariate beta type II distribution as well as the noncentral and bimatrix counterparts with positive domain. These models emanate from a sequential quality monitoring procedure with the normal and multivariate normal distributions as the underlying process distributions. Three different scenarios are considered, namely: 1. The variance is monitored from a normal process and the mean remains unchanged; 2. The above-mentioned scenario but the known mean also encounters a sustained shift; 3. The covariance structure of a multivariate normal distribution is monitored with the known mean vector unchanged. The statistics originating from the above-mentioned scenarios considered are constructed from different dependent chi-squared or Wishart ratios. Exact expressions are derived for the probability density functions of these statistics. These new distributions contribute to the statistical discipline in the sense that it can serve as alternatives to existing probability models, and can be used in determining the performance of the quality monitoring procedure.Thesis (PhD)--University of Pretoria, 2013.gm2014Statisticsunrestricte

Capturing a change in the covariance structure of a multivariate process

This research is inspired from monitoring the process covariance structure of q attributes where samples are independent, having been collected from a multivariate normal distribution with known mean vector and unknown covariance matrix. The focus is on two matrix random variables, constructed from different Wishart ratios, that describe the process for the two consecutive time periods before and immediately after the change in the covariance structure took place. The product moments of these constructed random variables are highlighted and set the scene for a proposed measure to enable the practitioner to calculate the run-length probability to detect a shift immediately after a change in the covariance matrix occurs. Our results open a new approach and provides insight for detecting the change in the parameter structure as soon as possible once the underlying process, described by a multivariate normal process, encounters a permanent/sustained upward or downward shift.University of Pretoria; National Research Foundation; National Research Foundation: SARChI Research Chair, as well as the Centre of Excellence in Mathematical and Statistical Sciences at the University of the Witwatersrand.https://www.mdpi.com/journal/symmetryam2023Statistic