Tag Archives: Parameter

On A Closed-Form Estimator of the Shape Parameter of the Three-Parameter Weibull Distribution (Published)

The shape parameter of the three-parameter Weibull distribution () was considered in this study. Known estimation methods like the maximum likelihood, method of moment and maximum product of spacing do not have closed-form estimators for the shape parameter of the three-parameter Weibull distribution rather they involve iterative procedures which may be time-consuming and are less tractable. Dubey (1967), Goda et al (2010) and Teimouri and Gupta (2013) have proposed closed-form estimators for . In this study, a closed-form estimator for  is proposed and the proposed estimator is compared with the existing closed-form estimators proposed by the authors mentioned above. To compare the accuracy of the estimators, Monte Carlo simulation is performed. Simulated data from the Weibull distribution are used to check the accuracy of the estimators and the root mean square error (RMSE) is used as a metric for accuracy. The results show that in general, the proposed estimator performs better than the other three closed-form estimators that were compared.

Keywords: Accuracy, Estimators, Parameter, tractability, weibull

Parameter Sensitivity and Elasticity Analysis of a Mathematical Model for Non–Homogenous Population Density of a Weed Species (Published)

In this work, a stage-structured model for non- homogenous population density of an annual weed is analysed for parameter sensitivity and elasticity. The steady state solution of the model is obtained. In order to determine the contribution of identified parameters to the model steady state, the sensitivity and elasticity analyses are performed using matrix calculus approach. The result of the sensitivity analysis shows that the steady state is very responsive to change in established seedling survival rate (e). While, elasticity analysis indicates that, both established and matured weeds steady-state densities are equally affected by small additive changes in maturity rate (m) and establishment rate (e). Besides, seed bank seed density is most sensitive to small additive change in seed production (b) as compared to weed maturity rate (m). Hence, we conclude that increase in the survival and maturity rates possibly may lead to an increase in weed population density.

Keywords: Elasticity, Matrix calculus, Parameter, Partial derivative., Steady-state, sensitivity