Update base test class for beta distribution

Added exceptions when parameters are not strictly positive.

Do not raise an exception for x=0 or x=1 when alpha or beta<1 and return
the limit.

Add special cases for x=0 and x=1 when alpha or beta = 1.

commons-statistics-distribution/src/main/java/org/apache/commons/statistics/distribution/BetaDistribution.java

@@ -40,6 +40,13 @@ public class BetaDistribution extends AbstractContinuousDistribution {
      */
     public BetaDistribution(double alpha,
                             double beta) {
+        if (alpha <= 0) {
+            throw new DistributionException(DistributionException.NOT_STRICTLY_POSITIVE, alpha);
+        }
+        if (beta <= 0) {
+            throw new DistributionException(DistributionException.NOT_STRICTLY_POSITIVE, beta);
+        }
+
         this.alpha = alpha;
         this.beta = beta;
         z = LogGamma.value(alpha) + LogGamma.value(beta) - LogGamma.value(alpha + beta);
@@ -63,28 +70,48 @@ public double getBeta() {
         return beta;
     }
 
-    /** {@inheritDoc} */
+    /** {@inheritDoc}
+     *
+     * <p>The density is not defined when {@code x = 0, alpha < 1}, or {@code x = 1, beta < 1}.
+     * In this case the limit of infinity is returned.
+     */
     @Override
     public double density(double x) {
         return Math.exp(logDensity(x));
     }
 
-    /** {@inheritDoc} **/
+    /** {@inheritDoc}
+     *
+     * <p>The density is not defined when {@code x = 0, alpha < 1}, or {@code x = 1, beta < 1}.
+     * In this case the limit of infinity is returned.
+     */
     @Override
     public double logDensity(double x) {
         if (x < 0 ||
             x > 1) {
             return Double.NEGATIVE_INFINITY;
         } else if (x == 0) {
             if (alpha < 1) {
-                throw new DistributionException(DistributionException.TOO_SMALL,
-                                                alpha, 1.0);
+                // Distribution is not valid when x=0, alpha<0
+                // due to a divide by zero error.
+                // Do not raise an exception and return the limit.
+                return Double.POSITIVE_INFINITY;
+            }
+            // Special case of cancellation: x^(a-1) (1-x)^(b-1) / B(a, b)
+            if (alpha == 1) {
+                return -z;
             }
             return Double.NEGATIVE_INFINITY;
         } else if (x == 1) {
             if (beta < 1) {
-                throw new DistributionException(DistributionException.TOO_SMALL,
-                                                beta, 1.0);
+                // Distribution is not valid when x=1, beta<0
+                // due to a divide by zero error.
+                // Do not raise an exception and return the limit.
+                return Double.POSITIVE_INFINITY;
+            }
+            // Special case of cancellation: x^(a-1) (1-x)^(b-1) / B(a, b)
+            if (beta == 1) {
+                return -z;
             }
             return Double.NEGATIVE_INFINITY;
         } else {

commons-statistics-distribution/src/test/resources/org/apache/commons/statistics/distribution/test.beta.1.properties

@@ -0,0 +1,23 @@
+# Licensed to the Apache Software Foundation (ASF) under one or more
+# contributor license agreements.  See the NOTICE file distributed with
+# this work for additional information regarding copyright ownership.
+# The ASF licenses this file to You under the Apache License, Version 2.0
+# (the "License"); you may not use this file except in compliance with
+# the License.  You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+parameters = 0.1 0.1
+# Computed using Matlab
+mean = 0.5
+variance = 0.208333333333333
+lower = 0
+upper = 1
+cdf.points = -0.1, 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1
+cdf.values = 0  0 0.406385093936276 0.439709190223346 0.462804186115552 0.482120045609328 0.500000000000000 0.517879954390672 0.537195813884448 0.560290809776654 0.593614906063724 1 1
+pdf.values = 0  Infinity 0.442988958666524 0.263938762316795 0.206639715373253 0.183240320487425 0.176630277977874 0.183240320487425 0.206639715373253 0.263938762316795 0.442988958666524 Infinity 0

commons-statistics-distribution/src/test/resources/org/apache/commons/statistics/distribution/test.beta.10.properties

@@ -0,0 +1,23 @@
+# Licensed to the Apache Software Foundation (ASF) under one or more
+# contributor license agreements.  See the NOTICE file distributed with
+# this work for additional information regarding copyright ownership.
+# The ASF licenses this file to You under the Apache License, Version 2.0
+# (the "License"); you may not use this file except in compliance with
+# the License.  You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+parameters = 0.5 4.0
+# Computed using Matlab
+mean = 0.111111111111111
+variance = 0.017957351290685
+lower = 0
+upper = 1
+cdf.points = -0.1, 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1
+cdf.values = 0  0 0.626625082597741 0.804984471899925 0.898778484206134 0.950264436880598 0.977796095859523 0.991483736629099 0.997455625383593 0.999522385942406 0.999971488851370 1 1
+pdf.values = 0  Inf 2.52142232809988  1.25219806739988  0.684938469046825 0.373544048607390 0.193349510480697 0.0903696114115064  0.0352965948694063  0.00978279740156159 0.00115291373026972 0 0

commons-statistics-distribution/src/test/resources/org/apache/commons/statistics/distribution/test.beta.11.properties

@@ -0,0 +1,23 @@
+# Licensed to the Apache Software Foundation (ASF) under one or more
+# contributor license agreements.  See the NOTICE file distributed with
+# this work for additional information regarding copyright ownership.
+# The ASF licenses this file to You under the Apache License, Version 2.0
+# (the "License"); you may not use this file except in compliance with
+# the License.  You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+parameters = 1.0 0.1
+# Computed using Matlab
+mean = 0.909090909090909
+variance = 0.039354584809130
+lower = 0
+upper = 1
+cdf.points = -0.1, 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1
+cdf.values = 0  0 0.0104807417937856  0.0220672314570715  0.0350389048801824  0.0497997834943236  0.0669670084631926  0.0875564634445192  0.113431849434787 0.148660077479215 0.205671765275719 1 1
+pdf.values = 0  0.100000000000000 0.109946584245135 0.122241596067866 0.137851585017117 0.158366702750946 0.186606598307362 0.228110884138870 0.295522716855071 0.425669961260392 0.794328234724282 Inf 0

commons-statistics-distribution/src/test/resources/org/apache/commons/statistics/distribution/test.beta.12.properties

@@ -0,0 +1,23 @@
+# Licensed to the Apache Software Foundation (ASF) under one or more
+# contributor license agreements.  See the NOTICE file distributed with
+# this work for additional information regarding copyright ownership.
+# The ASF licenses this file to You under the Apache License, Version 2.0
+# (the "License"); you may not use this file except in compliance with
+# the License.  You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+parameters = 1.0 0.5
+# Computed using Matlab
+mean = 0.66666666666666663
+variance = 0.088888888888888892
+lower = 0
+upper = 1
+cdf.points = -0.1, 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1
+cdf.values = 0 0 0.051316701949486218 0.10557280900008409 0.16333997346592444 0.22540333075851654 0.2928932188134527 0.36754446796632401 0.45227744249483381 0.55278640450004213 0.68377223398316211 1 1
+pdf.values = 0 0.5 0.52704627669472992 0.55901699437494745 0.59761430466719689 0.64549722436790291 0.70710678118654768 0.79056941504209488 0.9128709291752769 1.1180339887498951 1.58113883008419 Inf 0

commons-statistics-distribution/src/test/resources/org/apache/commons/statistics/distribution/test.beta.13.properties

@@ -0,0 +1,23 @@
+# Licensed to the Apache Software Foundation (ASF) under one or more
+# contributor license agreements.  See the NOTICE file distributed with
+# this work for additional information regarding copyright ownership.
+# The ASF licenses this file to You under the Apache License, Version 2.0
+# (the "License"); you may not use this file except in compliance with
+# the License.  You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+parameters = 1.0 1.0
+# Computed using Matlab
+mean = 0.5
+variance = 0.083333333333333329
+lower = 0
+upper = 1
+cdf.points = -0.1, 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1
+cdf.values = 0.0, 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.0
+pdf.values = 0 1 1 1 1 1 1 1 1 1 1 1 0

commons-statistics-distribution/src/test/resources/org/apache/commons/statistics/distribution/test.beta.14.properties

@@ -0,0 +1,23 @@
+# Licensed to the Apache Software Foundation (ASF) under one or more
+# contributor license agreements.  See the NOTICE file distributed with
+# this work for additional information regarding copyright ownership.
+# The ASF licenses this file to You under the Apache License, Version 2.0
+# (the "License"); you may not use this file except in compliance with
+# the License.  You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+parameters = 1.0 2.0
+# Computed using Matlab
+mean = 0.33333333333333331
+variance = 0.055555555555555552
+lower = 0
+upper = 1
+cdf.points = -0.1, 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1
+cdf.values = 0 0 0.19000000000000006 0.35999999999999999 0.51000000000000023 0.64000000000000001 0.75 0.83999999999999997 0.90999999999999992 0.95999999999999996 0.98999999999999999 1 1
+pdf.values = 0 2 1.8 1.6000000000000001 1.3999999999999999 1.2 1 0.80000000000000004 0.60000000000000009 0.39999999999999991 0.19999999999999996 0 0

commons-statistics-distribution/src/test/resources/org/apache/commons/statistics/distribution/test.beta.15.properties

@@ -0,0 +1,23 @@
+# Licensed to the Apache Software Foundation (ASF) under one or more
+# contributor license agreements.  See the NOTICE file distributed with
+# this work for additional information regarding copyright ownership.
+# The ASF licenses this file to You under the Apache License, Version 2.0
+# (the "License"); you may not use this file except in compliance with
+# the License.  You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+parameters = 1.0 4.0
+# Computed using Matlab
+mean = 0.20000000000000001
+variance = 0.026666666666666672
+lower = 0
+upper = 1
+cdf.points = -0.1, 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1
+cdf.values = 0 0 0.34389999999999987 0.59040000000000026 0.75990000000000002 0.87040000000000006 0.9375 0.97440000000000004 0.9919 0.99839999999999995 0.99990000000000001 1 1
+pdf.values = 0 4 2.9160000000000008 2.0480000000000005 1.3719999999999999 0.8640000000000001 0.50000000000000022 0.25600000000000012 0.10800000000000005 0.031999999999999994 0.0039999999999999983 0 0

commons-statistics-distribution/src/test/resources/org/apache/commons/statistics/distribution/test.beta.16.properties

@@ -0,0 +1,23 @@
+# Licensed to the Apache Software Foundation (ASF) under one or more
+# contributor license agreements.  See the NOTICE file distributed with
+# this work for additional information regarding copyright ownership.
+# The ASF licenses this file to You under the Apache License, Version 2.0
+# (the "License"); you may not use this file except in compliance with
+# the License.  You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+parameters = 2.0 0.1
+# Computed using Matlab
+mean = 0.95238095238095233
+variance = 0.01462950771706532
+lower = 0
+upper = 1
+cdf.points = -0.1, 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1
+cdf.values = 0 0 0.00058554921172346416 0.0025085760862129224 0.0060900720265878658 0.011791774834096561 0.020315358886352223 0.032809851251190306 0.051372078895221711 0.080552883677552423 0.13418222415053294 1 1
+pdf.values = 0 0 0.012094124266964851 0.026893151134930546 0.045491023055648561 0.069681349210416327 0.10263362906904888 0.15055318353165442 0.22755249197840488 0.37458956590914555 0.78638495237703931 Inf 0

commons-statistics-distribution/src/test/resources/org/apache/commons/statistics/distribution/test.beta.17.properties

@@ -0,0 +1,23 @@
+# Licensed to the Apache Software Foundation (ASF) under one or more
+# contributor license agreements.  See the NOTICE file distributed with
+# this work for additional information regarding copyright ownership.
+# The ASF licenses this file to You under the Apache License, Version 2.0
+# (the "License"); you may not use this file except in compliance with
+# the License.  You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+parameters = 2.0 0.5
+# Computed using Matlab
+mean = 0.80000000000000004
+variance = 0.045714285714285714
+lower = 0
+upper = 1
+cdf.points = -0.1, 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1
+cdf.values = 0 0 0.0038825370469605129 0.016130089900092535 0.0378409694858131 0.070483996910219962 0.1161165235168156 0.17780780835622126 0.26057454736802566 0.37390096630005898 0.54146973927558506 1 1
+pdf.values = 0 0 0.079056941504209499 0.16770509831248426 0.26892643710023856 0.38729833462074181 0.53033008588991071 0.71151247353788538 0.95851447563404069 1.3416407864998741 2.1345374206136567 Inf 0

commons-statistics-distribution/src/test/resources/org/apache/commons/statistics/distribution/test.beta.18.properties

@@ -0,0 +1,23 @@
+# Licensed to the Apache Software Foundation (ASF) under one or more
+# contributor license agreements.  See the NOTICE file distributed with
+# this work for additional information regarding copyright ownership.
+# The ASF licenses this file to You under the Apache License, Version 2.0
+# (the "License"); you may not use this file except in compliance with
+# the License.  You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+parameters = 2.0 1.0
+# Computed using Matlab
+mean = 0.66666666666666663
+variance = 0.055555555555555552
+lower = 0
+upper = 1
+cdf.points = -0.1, 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1
+cdf.values = 0 0 0.010000000000000009 0.040000000000000029 0.089999999999999983 0.16000000000000003 0.25000000000000006 0.35999999999999999 0.48999999999999977 0.64000000000000012 0.81000000000000005 1 1
+pdf.values = 0 0 0.20000000000000007 0.40000000000000002 0.59999999999999987 0.80000000000000004 1 1.2 1.3999999999999999 1.6000000000000001 1.8 2 0

commons-statistics-distribution/src/test/resources/org/apache/commons/statistics/distribution/test.beta.19.properties

@@ -0,0 +1,23 @@
+# Licensed to the Apache Software Foundation (ASF) under one or more
+# contributor license agreements.  See the NOTICE file distributed with
+# this work for additional information regarding copyright ownership.
+# The ASF licenses this file to You under the Apache License, Version 2.0
+# (the "License"); you may not use this file except in compliance with
+# the License.  You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+parameters = 2.0 2.0
+# Computed using Matlab
+mean = 0.5
+variance = 0.049999999999999996
+lower = 0
+upper = 1
+cdf.points = -0.1, 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1
+cdf.values = 0 0 0.028000000000000008 0.10400000000000008 0.2159999999999998 0.35200000000000004 0.5 0.64799999999999991 0.78400000000000003 0.89600000000000002 0.97199999999999998 1 1
+pdf.values = 0 0 0.54000000000000004 0.96000000000000008 1.2599999999999998 1.4400000000000002 1.5 1.4400000000000002 1.26 0.95999999999999985 0.53999999999999981 0 0

commons-statistics-distribution/src/test/resources/org/apache/commons/statistics/distribution/test.beta.2.properties

@@ -0,0 +1,23 @@
+# Licensed to the Apache Software Foundation (ASF) under one or more
+# contributor license agreements.  See the NOTICE file distributed with
+# this work for additional information regarding copyright ownership.
+# The ASF licenses this file to You under the Apache License, Version 2.0
+# (the "License"); you may not use this file except in compliance with
+# the License.  You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+parameters = 0.1 0.5
+# Computed using Matlab
+mean = 0.166666666666667
+variance = 0.086805555555556
+lower = 0
+upper = 1
+cdf.points = -0.1, 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1
+cdf.values = 0  0 0.704833622051221 0.759304219445319 0.795176530367368 0.823494838536657 0.848001712399770 0.870603436980005 0.892658587836406 0.915640640375004 0.942366288315790 1 1
+pdf.values = 0  Infinity 0.739458664410644 0.420303655461325 0.311944266317603 0.260079151351645 0.233065049073820 0.221140881157234 0.222272786172717 0.241401058813832 0.307055512274369 Infinity 0