S1 Appendix -

(DOCX)</p

Comparison with a p-value of KS, <i>A</i>² and <i>W</i> statistics in different methods.

Comparison with a p-value of KS, A2 and W statistics in different methods.</p

Estimated value of parameters: Proposed as well as competitive models.

Estimated value of parameters: Proposed as well as competitive models.</p

Estimated parameters’ value from four different methods.

Estimated parameters’ value from four different methods.</p

Descriptive characteristic of the proposed model.

Descriptive characteristic of the proposed model.</p

Estimated fitted CDF (left panel), Estimated fitted densities (right panel).

Estimated fitted CDF (left panel), Estimated fitted densities (right panel).</p

Estimated parameter values of all competitive models.

Estimated parameter values of all competitive models.</p

Comparison of -2LL, AIC, BIC, CIAC, and HQIC value among models.

Comparison of -2LL, AIC, BIC, CIAC, and HQIC value among models.</p

Calculated value of -2LL, AIC, BIC, CIAC, and HQIC of different models.

Calculated value of -2LL, AIC, BIC, CIAC, and HQIC of different models.</p

Estimated fitted CDF (left panel), Estimated fitted densities (right panel) of carbon fiber data set.

Estimated fitted CDF (left panel), Estimated fitted densities (right panel) of carbon fiber data set.</p