The Partial L-Moment of the Four Kappa Distribution

Statistical analysis of extreme events such as flood events is often carried out to predict large return period events. The behaviour of extreme events not only involves heavy-tailed distributions but also skewed distributions, similar to the four-parameter Kappa distribution (K4D). In general, this covers many extreme distributions such as the generalized logistic distribution (GLD), the generalized extreme value distribution (GEV), the generalized Pareto distribution (GPD), and so on. To utilize these distributions, we have to estimate parameters accurately. There are many parameter estimation methods, for example, Method of Moments, Maximum Likelihood Estimator, L-Moments, or partial L-Moments. Nowadays, no researchers have applied the partial L-Moments method to estimate the parameters of K4D. Therefore, the objective of this paper is to derive the partial L-Moments (PL-Moments) for K4D, namely the PL-Moments of the K4D in order to estimate hydrological extremes from censored data. The findings of this paper are formulas of parameter estimation for K4D based on the PL-Moments approach. We have derived the Partial Probability-Weighted Moments (PPWMs) of the K4D (β'r) and derive the estimation of parameters when separated by shape parameters (k,h) conditions i.e., case k>-1 and h>0, case k>-1 and h=0 and case -1<k<-1/h and h<0. Finally, we expect that the parameter estimate for K4D from this formula will help to make accurate forecasts. Doi: 10.28991/ESJ-2023-07-04-06 Full Text: PD

Parameter Estimation of Power Function Distribution with TL-moments

Accurate estimation of parameters of a probability distribution is of immense importance in statistics. Biased and imprecise estimation of parameters can lead to erroneous results. Our focus is to estimate the parameter of Power function distribution accurately because this density is now widely used for modelling various types of data.  In this study, L-moments, TL-moments, LL-moments and LH-moments of Power function distribution are derived. In addition, the coefficient of variation, skewness and kurtosis are obtained by method of moments, L-moments and TL-moments. Parameters of the density are estimated using linear moments and compared with method of moments and MLE on the basis of bias, root mean square error and coefficients through simulation study. L-moments proved to be superior for the parameter estimation and this conclusion is equally true for different parametric values and sample size.La distribución de función de potencias es ampliamente usada. Dada su importancia, es necesario estimar sus parámetros de manera precisa. En este artículo, los momentos TL de la distribución de función de potencias son derivados así como sus casos especiales tales como los momentos L, LL y LH. Los coeficientes de variación, sesgo y curtosis son obtenidos a partir de los momentos L y TL. Los parámetros desconocidos son estimados y los momentos lineales son comparados con el método de momentos y estimadores máximo verosímiles en la base del sesgo, raíz del error cuadrático medio a través de un estudio de simulación. Los momentos L permiten obtener estimaciones más precisas y esta conclusión es verdad para diferentes valores paramétricos y tamaño de muestra

The dynamics underlying the rise of star performers

Across different domains, there are ‘star performers’ who are able to generate disproportionate levels of performance output. To date, little is known about the model principles underlying the rise of star performers. Here, we propose that star performers' abilities develop according to a multi-dimensional, multiplicative and dynamical process. Based on existing literature, we defined a dynamic network model, including different parameters functioning as enhancers or inhibitors of star performance. The enhancers were multiplicity of productivity, monopolistic productivity, job autonomy, and job complexity, whereas productivity ceiling was an inhibitor. These enhancers and inhibitors were expected to influence the tail-heaviness of the performance distribution. We therefore simulated several samples of performers, thereby including the assumed enhancers and inhibitors in the dynamic networks, and compared their tail-heaviness. Results showed that the dynamic network model resulted in heavier and lighter tail distributions, when including the enhancer- and inhibitor-parameters, respectively. Together, these results provide novel insights into the dynamical principles that give rise to star performers in the population

Symbolic computation of moments of sampling distributions

By means of the notion of umbrae indexed by multisets, a general method to express estimators and their products in terms of power sums is derived. A connection between the notion of multiset and integer partition leads immediately to a way to speed up the procedures. Comparisons of computational times with known procedures show how this approach turns out to be more efficient in eliminating much unnecessary computation.Comment: 21 pages, 7 table

Quantile Approximation of the Erlang Distribution using Differential Evolution Algorithm

Erlang distribution is a particular case of the gamma distribution and is often used in modeling queues, traffic congestion in wireless sensor networks, cell residence duration and finding the optimal queueing model to reduce the probability of blocking. The application is limited because of the unavailability of closed-form expression for the quantile (inverse cumulative distribution) function of the distribution. The problem is primarily tackled using approximation since the inversion method cannot be applied. This paper extended a six parameter quantile model earlier proposed to the Nakagami distribution to the Erlang distributions. Consequently, the established relationship between the two distributions is now extended to their quantile functions. The quantile model was used to fit the machine (R software) values with their corresponding quartiles in two ways. Firstly, artificial neural network (ANN) was used to establish that a curve fitting can be achieved. Lastly, differential evolution (DE) algorithm was used to minimize the errors obtained from the curve fitting and hence estimate the values of the six parameters of the quantile model that will ensure the best possible fit, for different values of the parameters that characterize Erlang distribution. Hence, the problem is constrained optimization in nature and the DE algorithm was able to find the different values of the parameters of the quantile model. The simulation result corroborates theoretical findings. The work is a welcome result for the quest for a universal quantile model that can be applied to different distributions