Malaysian Women Shoe Sizing System Using Multivariate Normal Probability Distribution

Abstract

The Malaysian women population frequently face the problem of finding the best fitting shoes. This problem is created by the absence of a Malaysian women shoe sizing system. Standard statistical methods involving the Multivariate Normal distribution are used in a novel process of addressing issues related to the creation of a shoe sizing system, in particular, the problem of defining categories of shoe sizes. This study focused on the use of five-foot measurement namely, foot length (FL), foot breadth (FB), foot's ball girth (BG), instep length (IL), and fibulare instep length (FIL). Univariate hypothesis testing was performed taking advantage of the existence of normal probability distribution. For brevity, details for FL, FB, and BG are shown in this paper, followed by a comparison of performance results between (FL, FB, BG) and (FL, FB, BG, IL, FIL). Our results were compared to a similar study showing almost the same aggregate loss and coverage percentage. The result shows that a modest sample size of 160 was sufficient to define categories of shoe sizes to help develop a prototype shoe sizing system using the proposed novel approach. The proposed prototype shoe sizing system provides information for the planning, design, and manufacturing of Malaysian women's footwear with implications for better fitness and comfort.

Keywords

• Shoe size variation
• clustering analysis
• mixture distribution
• hypothesis testing
• shoe sizing system