Table 2 Simulations results for values of k = 0.1 and h = 0.8.

From: A comparative analysis of L-moments, maximum likelihood, and maximum product of spacing methods for the four-parameter kappa distribution in extreme value analysis

Methods of Estimation

Parameters

n = 20

n = 40

n = 75

n = 100

n = 200

RMSE

Bias

RMSE

Bias

RMSE

Bias

RMSE

Bias

RMSE

Bias

LM

\(\:\epsilon\:\)

3.9238

−3.2683

1.0071

−0.3839

0.4517

−0.1181

0.3326

−0.0621

0.1854

−0.0052

\(\:\theta\:\)

6.4600

5.4247

1.3791

0.4401

0.568

0.1478

0.39

0.0859

0.228

0.015

K

0.8930

0.7948

0.2638

0.0516

0.1980

0.0321

0.1470

0.0208

0.1026

−0.0045

H

1.1167

0.0517

0.6349

0.1619

0.4280

0.0313

0.3386

0.0140

0.2098

−0.0173

MLE

\(\:\epsilon\:\)

1.3031

−1.164

1.3735

−0.8295

0.4849

−0.2332

0.3439

−0.1300

0.1366

−0.038

\(\:\theta\:\)

2.9525

2.2641

2.0332

1.2175

0.6982

0.352

0.4829

0.2074

0.2045

0.0546

K

0.8686

0.6922

0.3691

0.2881

0.2365

0.1261

0.1761

0.0880

0.0922

0.0223

H

0.7240

0.5238

0.6651

0.4038

0.3518

0.1616

0.2558

0.1001

0.1248

0.0357

MPS

\(\:\epsilon\:\)

0.7771

−0.4771

0.3517

0.1842

0.2555

0.0267

0.2043

0.0095

0.1141

0.0265

\(\:\theta\:\)

0.5314

0.5313

0.3067

−0.2911

0.31

−0.0364

0.2673

0.0032

0.1682

−0.0352

K

0.1542

0.1542

0.1912

−0.1556

0.1793

−0.0566

0.1414

−0.0310

0.0959

−0.0432

H

0.7039

0.2540

0.4856

−0.3028

0.3476

−0.0987

0.2255

−0.0417

0.1317

−0.0433

  1. Note: The lowest values of RMSE and Bias for “k” and “h” and different sample sizes are highlighted in red.