$client = new SoapClient($wsdlUrl);
$newsletterStatisticRequest = new StdClass();
$newsletterStatisticRequest->mandatorId = 0;
$newsletterStatisticRequest->newsletterIds = array(1);
try {
  $result = $client->NewsletterStatistic($newsletterStatisticRequest);
  var_dump($result);
} catch (Exception $e) {
  echo "Fehler aufgetreten: " . $e->getMessage() . "\r\n";
}

object(stdClass)#3 (1) {
  ["newsletterStatistic"]=>
  object(stdClass)#4 (26) {
    ["newsletterId"]=>
    int(1)
    ["newsletterListId"]=>
    int(1)
    ["newsletterStatus"]=>
    int(3)
    ["mailsPerHour"]=>
    int(1800)
    ["mailsPerHourIncludeErrors"]=>
    int(203)
    ["sendStartTime"]=>
    string(29) "2012-10-29T11:13:00.000+01:00"
    ["sendBeginTime"]=>
    string(29) "2012-10-29T11:14:34.000+01:00"
    ["sendLastTime"]=>
    string(29) "2012-10-29T11:15:27.000+01:00"
    ["sendEndTime"]=>
    string(29) "2012-10-29T11:14:40.000+01:00"
    ["sendedByInternalMta"]=>
    bool(true)
    ["newsletterListName"]=>
    string(15) "Testverteiler 1"
    ["newsletterSubject"]=>
    string(22) "Newslettertest"
    ["newsletterDescription"]=>
    string(22) "Newslettertest"
    ["numErrorHandlingActive"]=>
    int(0)
    ["numRecipientsUnadjusted"]=>
    int(6)
    ["numRecipientsAdjusted"]=>
    int(3)
    ["numSend"]=>
    int(3)
    ["numSuccess"]=>
    int(3)
    ["sendDuration"]=>
    int(6)
    ["sendDurationIncludeErrors"]=>
    int(53)
    ["numTemporaryErrors"]=>
    int(0)
    ["numPermanentErrors"]=>
    int(0)
    ["numTemporaryDomainErrors"]=>
    int(0)
    ["numPermanentDomainErrors"]=>
    int(0)
    ["numUnhandledErrors"]=>
    int(0)
    ["invalidSubscriberInfo"]=>
    object(stdClass)#5 (10) {
      ["invalidTargetGroupSubsscribers"]=>
      int(0)
      ["numSubscribersRemoved"]=>
      int(0)
      ["invalidEmails"]=>
      int(0)
      ["blockedByTempRobinson"]=>
      int(2)
      ["blockedByExternalRobinson"]=>
      int(0)
      ["blockedByProfileFilter"]=>
      int(0)
      ["blockedByBackclickFilter"]=>
      int(0)
      ["blockedByNewsletterLists"]=>
      int(0)
      ["blockedByComplaintList"]=>
      int(0)
      ["blockedByFreeRobinsonList"]=>
      int(0)
    }
  }
}

$client = new SoapClient($wsdlUrl);
$newsletterStatisticRequest = new StdClass();
$newsletterStatisticRequest->mandatorId = 0;
$newsletterStatisticRequest->newslettersInPeriod = new StdClass();
$newsletterStatisticRequest->newslettersInPeriod->newsletterListId = 1;
$newsletterStatisticRequest->newslettersInPeriod->timePeriod = new StdClass();
date_default_timezone_set('Europe/Berlin');
$newsletterStatisticRequest->newslettersInPeriod->timePeriod->startTime = mktime(13, 10, 0, 10, 30, 2012);
$newsletterStatisticRequest->newslettersInPeriod->timePeriod->endTime = mktime(13, 19, 0, 10, 30, 2012);
try {
  $result = $client->NewsletterStatistic($newsletterStatisticRequest);
  var_dump($result);
} catch (Exception $e) {
  echo "Fehler aufgetreten: " . $e->getMessage() . "\r\n";
}