Following code:

import java.util.*;

public class Test {

    public static void main(String[] args) {
        StringJoiner expected = new StringJoiner("\n");
        expected.add("expected:");

        StringJoiner actual = new StringJoiner("\n");
        actual.add("actual:");

        Iterator<Double> i = new SplittableRandom(0).doubles(8).distinct().iterator();
        while (i.hasNext()) {
            expected.add(String.valueOf(i.next()));
        }

        i = new SplittableRandom(0).doubles(8).distinct().parallel().iterator();
        while (i.hasNext()) {
            actual.add(String.valueOf(i.next()));
        }

        System.out.println(expected);
        System.out.println(actual);
    }
}

Produces following output:

expected:
0.6118225421857174
0.8243869101616611
0.8435259660697864
0.4175532166907524
0.1350922166954046
0.13871074418376472
0.24279104418383668
0.2419412935695664
actual:
0.10047975177649981
0.4886723680988455
0.24952460161236745
0.2001101735985169
0.4175532166907524
0.8603064296150352
0.7058812188621817
0.13950492113400426

However we should have received the identical result according to following assertion from specification:

Except for operations identified as explicitly nondeterministic, such as findAny(), whether a stream executes sequentially or in parallel should not change the result of the computation.

This assertion could be found here:
http://jre.us.oracle.com/java/re/jdk/8/promoted/latest/doc/api/java/util/stream/package-summary.html