This　research　examines　how　degrees　of　freedom　and　covariance　matrix　configurations　affect　Wishart　distributed　matrix　eigenvalue　distributions.　We　use　the　energy　distance　metric　to　compare　eigenvalue　distributions　in　Identity,　Diagonal,　and　Structured　covariance　matrices.　Through　extensive　simulations,　we　show　that　degrees　of　freedom　and　covariance　matrix　architectures　greatly　affect　eigenvalue　dispersion　and　energy　distance　distributions.　Statistical　models　are　more　reliable　with　smaller,　more　stable　distributions　from　higher　degrees　of　freedom.　We　analyze　the　eigenvalue　distributions　of　NextEra　Energy　(NEE),　Enphase　Energy　(ENPH),　First　Solar　(FSLR),　SunPower　(SPWR),　and　Brookfield　Renewable　Partners　(BEP)　stocks　using　this　analytical　methodology.　Daily　returns　and　covariance　matrices　were　calculated　using　daily　closing　prices　from　January　1,　2018,　to　January　1,　2023.　Our　findings　support　simulation　studies　indicating　larger　degrees　of　freedom　lead　to　more　stable　energy　distance　distributions.The　findings　of　this　study　are　useful　in　finance,　genetics,　and　environmental　studies,　where　stability　and　variability　of　the　covariance　structure　are　important.　The　requirement　for　higher-dimensional　settings　and　real-world　datasets　to　validate　the　theoretical　framework　are　our　research’s　constraints.　This　research　expands　Wishart　distribution　knowledge　and　provides　a　solid　analytical　foundation　for　data　analysis　and　model　fitting　in　numerous　scientific　fields.　©　2024　Randa　A.　Makled,　et　al.