[IEEE 2012 IEEE Symposium on Humanities, Science and Engineering Research (SHUSER) - Kuala Lumpur (2012.06.24-2012.06.27)] 2012 IEEE Symposium on Humanities, Science and Engineering

Islamic Inheritance Claim Processes - Non-Normality Data Traits and Best Estimator Choice

*Noraini Noordin, *Adibah Shuib, *Mohamad Said Zainol and **Mohamed Azam Mohamed Adil *Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, Malaysia ** Centre of Islamic Thoughts and Understanding, Universiti Teknologi MARA, Malaysia

[email protected], [email protected], [email protected], [email protected]

Abstract— To confront and combat some of the issues in the administration and distribution of Islamic inheritance, Muslims have to look pass constitutional amendments and consider other alternatives as practical solutions to the problem of lengthy and costly claim procedures. Unveiling the uncertainties and confusion undergone by Muslims for so many years has provided the basis for our study to develop the network model and the mathematical model as solution approach to this problem. Careful analysis of variables using normality tests, descriptive statistics, normal and detrended plots as well as box-plots confirms the non-normality of variables, a finding upon which is built the assumption to use median absolute deviation as the best measure of variation to estimate activity durations of the model.

Keywords- Network Flow Model; Descriptive Statistics; Median absolute deviation; Non-normality

I. INTRODUCTION Developing a model, acquiring input data, developing a

solution and testing the solution are four crucial interrelated factors of the quantitative approach to decision making. Analysis of precedence relations between variables promotes the selection of models to be used for representation of a particular situation. Activities in the administration and distribution process of Islamic inheritance are performed either in series with each other or in parallel to each other. By representing these activities as a sequence of points connected together by paths in a network, the Islamic inheritance management and distribution process flows can be described as a network flow (NF) model.

Careful study of the erratic movements displayed by the Muslims in the process to claim inheritance reveals a high degree of uncertainty and confusion among them with regards to the correct procedures to follow, thus prompting the current study to look pass the constitutional amendments for a more practical alternative solution to the problem of delay and expensive costs associated with the claim processes in the administration and distribution of Islamic inheritance [1, 2]. Analysis of the predicaments faced by Muslims has also provided the momentum and the basis for the setting up of a NF model to represent this situation [2]. Therefore, this paper will highlight the more practical approach taken by the current study to address the prolonged agony faced by the Muslims in coping with inter-twining constitutional issues which affect the management of Islamic inheritance.

In addition, relevant details have to be input with care into this NF model so that it is solvable, realistic, easy to understand and to modify, and will incorporate inheritance data that is found. Hence, this paper will not only discuss the methods used in the study to define and classify variables involved as heavy tailed distributions but will also elaborate on how this classification affects the choice of statistic to estimate activity times in the NF model.

II. METHODOLOGY This section will share findings from the current study

on this new approach according to the following perspectives: i) summary of issues and problems in the administration and distribution of Islamic inheritance, ii) the importance of the NF model as a pictorial representation of precedence relations and also inter-dependencies of variables involved in the administration and distribution processes of Islamic inheritance, iii) the impact of characteristics of variables on the choice of best estimator for activity durations, and iv) justification for median absolute deviation as the best estimator for activity durations.

A. Summary of issues and problems in the administration and distribution of Islamic inheritance Preliminary data analysis on 516 inheritance cases in Perak

found the distribution of time differences between time of death and submission time of claim forms to be right-skewed due to the presence of many extreme values as shown in Fig. 1.

Figure 1. Stem-and-Leaf Plot for time durations between

Registration Date and Date of Death

2012 IEEE Symposium on Humanities, Science and Engineering Research

978-1-4673-1310-0/12/$31.00 ©2012 IEEE 635

To understand the impact this display has on the current study, further analysis of the characteristics of this variable is undertaken. Since the stem-and-leaf plot on time differences between registration date and time of death indicate the presence of many extreme values and mean is susceptible to extreme values, median (M) has been chosen to be used in this analysis [3]. M divides a data set into two halves and each of these halves can be further broken up into two other halves using the lower and upper hinge(H)s. In particular, the location of the letter values M and H within the data set is given by their depths, namely

��

�� ! �"� #��$%�� &�� &�� '�(�� ')"'�and �� ')"'�� ')�� *"', thus

i) ��&�� ')��'* �� +(��+(+� ��+(,��%�, ii) ��$��&�� *�

��-. � -** � ,�� ,.'"'��%�� iii) ��&�� -)+��-)) � /00/1/02/3 � '.�.��%�4 and iv) ��5��6�5'.�.�,.'"'6��%��,(.,"'��%�"

The above calculations find time taken to submit a claim form to the respective institutions to be approximately 1764 days from the time of death. Further calculations indicate that

v) ��7��5�"'×��6 �'.�.��"'×,(.,"' ��*�("+'��%�� vi) ��7��5-".8��6 �'.�.��-".8,(.,"' ��))�-"'��%�"��

Extreme observations in a data set can be shown in a schematic box plot, as moderate outliers if they lie outside the inner fence but within the outer fence while the extreme outliers lie outside the outer fence [3]. The above fences have classified data 484 (data value = 11994 days) to data 503 (data value = 17570 days) as moderate outliers and data 504 (data value = 19024 days) onwards as extreme outliers. These outliers represent approximately 6.4% of the inheritance cases and the claim forms for these inheritance cases are submitted to the respective institutions to be processed only after almost 33 years after the deceased has passed away.

Studies indicate that number of petitions lodged in the few years after the death of a person is very minimal; only about 20% of claims are submitted in the year of death and this percent value decreases for a period of twenty years before it rises back to the same value [4]. The time frame for settlement of inheritance cases is from three to ten years but there are cases that prolonged to more than twenty years [5].

Intertwining constitutional issues has been cited as one of the reasons for the delays in the claim processes [6, 7]. The impact these intertwining constitutional issues have on the movement patterns of Muslims through the claim processes will be discussed in the next section. In particular, Muslims have had to endure financial burden associated with similar time-consuming claim processes since independence in 1957. Table 1 displays descriptive statistics for estate values upon death and after submission of petition, and for amount of fee paid upon settlement of case involving 73 inheritance cases in Perak in 2010.

TABLE 1. DESCRIPTIVE STATISTICS SHOWING ESTATE VALUES AND SETTLEMENT FEES

N Min Max Mean SD Skewness KurtosisStatistic Statistic Statistic Statistic Statistic Statistic SE Statistic SE

Value upon death73 75.00 140488.20 17987.088 29408.71108 2.643 .281 7.113 .555

Value upon submission 73 1300.00 661574.19 77717.165 1.12517E5 3.215 .281 12.393 .555

Fee 71 10.00 1323.15 143.9751 225.82839 3.311 .285 13.101 .563Valid N (listwise)

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As expected, estate value increases with respect to time taken by Muslims to lodge a petition to claim inheritance and this increase in turn causes an increase in the amount of settlement fees to be paid since the fees paid are based on a certain percentage value of the estates .

Before the advent of IT, calculations for the Faraid certificates depended on manual calculations. E-government efforts to improve how the government operates and delivers public services include setting up IT advancements like e-Syariah, e-Faraid and e-Tapp in government offices handling Islamic inheritance, thus time to produce Faraid certificates are minimized. However, studies indicate a rising trend in the number of unclaimed inheritance in the country and report the existence of RM72 million worth of unclaimed inheritance [8]. Therefore, these advancements do not have much effect on minimizing the number of unclaimed inheritance .

Due to unforeseen outcomes of the conditions for independence from the British in 1957, Malaysia now runs on a Federal Constitution that consists of many British influences. In particular, the marginalization of the functions of the Syariah courts and the increase in authority vested onto Civil High Courts to handle Islamic inheritance affect the legal system and the administration and distribution of Islamic inheritance significantly [7, 9].

Table 2 provides a description of the changes in ceiling values of estates due to constitutional amendments from 1974 to 2009. As observed, there is a gap of twenty years between the last two amendments as compared to gap between the other amendments. Majority of cases are transferred to the Land Offices after the last amendment caused a mass re-categorization of estates from Normal Estates to Small Estates, however the number of inheritance cases is still not decreasing [10].


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TABLE 2. CEILING VALUES AFTER AMENDMENTS

YEAR CEILING VALUES OF ESTATES

SUPPORTING DOCUMENT BEFORE AFTER

% INCREASE

1974 RM10 000 RM25 000 150 Federal Government Gazette No. PN. PJ2

1977 RM25 000 RM50 000 100 Act 399 Amendment to Act 98

1982 RM50 000 RM300 000 500 Act A 533 Amendment 1982

1989 RM300 000 RM600 000 100 Act A 702 2009 RM600 000 RM2 million 233.33 Act A1331

It is obvious at this point in the discussion that constitutional amendments do not have the potential to produce a great impact on optimizing time and money spent on claim processes of Islamic inheritance. Therefore, there is a need to look pass the legal system for any other practical solutions that would be able to minimize time and money spent on claim processes. This paper wishes to highlight the contribution of this current study to find an alternative solution in the form of a NF model which is more practical for the Muslims and has the potential to optimize time and cost spent on claim processes.

B. Importance of the NF model as a pictorial representation of precedence relations and also interdependencies of variables involved in the administration and distribution processes of Islamic inheritance

Literature reviews have identified that majority of Muslims encounter problems when they want to compile documents to submit along with the claim forms [5, 11]. These Muslims are confused and have no knowledge of the proper processes to follow, thus they have no idea where to begin, how to proceed and which institution to head for during the process [5, 6, 11]. Their movements during the whole process are described as disorganized and chaotic, more so when documents are missing and have to be traced at many agencies. A Muslim can be seen abstracting a death certificate at the National Registration Department one minute and the next minute he can be seen in front of a Commissioner for Oaths trying to produce a Form of Declaration in place of an untraceable death certificate [5, 6, 11]. Unveiling these uncertainties and confusion that Muslims go through to petition rights to Islamic inheritance by studying the erratic movements of the Muslims through the claim processes have provided the basis for the formation of a NF model to represent the administration and distribution processes for Islamic inheritance [2, 12]. Fig. 1 provides a general picture of the three major phases of activities in a claim process at all authorized institutions for administration and distribution of Islamic inheritance.

This paper believes that a NF model that can represent the entire claim process with clarity will uplift the predicaments faced by the Muslims. There are two considerations to be given to these activities before a NF model can be built, namely i) determine the number of sub-routines that are needed in the NF model based on requirements for Syariah-compliance and ii) identification of serial and concurrent activities.

Figure 2. Major activities in a claim process

For example, the first three activities in the pre-submission phase define the obligatory duties a Muslim has to perform before distributing the Islamic inheritance, thus these activities have to be carefully mapped out onto the model to indicate the sequential relationships between them. In order to accommodate these requirements, this phase can be broken down into two sub-phases to indicate the separation between the first three duties and the fourth duty [12]. The fourth duty includes activities to verify death, to validate legal inheritors, and to confirm existence of estates respectively in accordance with the requirements for compliance to the three principles of al-mauruth, al-warith and al-muwarrith in the Syariah [2, 12] Fig. 2 provides the preliminary network for activities 7-13 to validate Small Estates, which are part of the activities in the second sub-phase of the pre-submission phase.

Figure 3. Preliminary network – Process to validate Small Estates

C. The impact of characteristics of variables on the choice of best estimator for activity durations

Data collected for this study include data from Land Offices and Syariah Courts in Perak which are used to

Pre-submission Phase • Settle funeral Expenses • Settle debts of the deceased • Execution of will • Compile documents to verify death, certify

legitimate heirs and confirm existence of estates

Submission • Lodge a petition • Valuation of Estates • Hearing • Order for Distribution

Post-submission • Plea (if any) • Repeat trial (if necessary) • Pay fee • Registration of ownership of estates


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describe the activity durations for the submission phase. This section will focus on the importance of determining the characteristics of data from both areas. Table 3 provides the results of normality tests for data from the Land Offices in Kuala Kangsar.

TABLE 3. NORMALITY TESTS FOR DATA FROM LAND OFFICE IN KUALA KANGSAR

Tests of Normality

Kolmogorov-Smirnova Shapiro-Wilk

Statistic df Sig. Statistic df Sig.

DIFF REGDATE AND FORMB .211 485 .000 .796 485 .000DIFF FORMBFORMC .155 485 .000 .649 485 .000DIFF REGD VL .298 485 .000 .487 485 .000DIFF VL V .203 485 .000 .641 485 .000DIFF FORMC NOTE .190 485 .000 .804 485 .000DIFF NOTE 1 NOTE 2 .392 485 .000 .205 485 .000DIFF NOTE 2 HEARING .353 485 .000 .259 485 .000DIFF HEARING RECEIPT .521 485 .000 .154 485 .000DIFF RECEIPT STATEMENT .263 485 .000 .616 485 .000DIFF RECEIPT AND COURT .263 485 .000 .617 485 .000a. Lilliefors Significance Correction

Table 3 reports Kolmogorov-Smirnov tests to be insignificant (value < 0.05) for the above data set, thus variables are non-normally distributed. The same results were reported for Ipoh. The non-normality conclusion is substantiated by results from other tests as reported in Table 4.

TABLE 4. OTHER SUPPORTING TESTS TO SUBSTANTIATE NON-NORMALITY CONCLUSION

TEST RESULTS CONCLUSION Descriptive Statistics like skewness and kurtosis

Values are positive and negative

Variables are either positive or negatively skewed

Normality tests after SPSS Replace Missing Values

Kolmogorov-Smirnov shows insignificant value less than 0.05

Variables are non-normally distributed

Normality after outliers are removed according to Z-scores not exceeding ± 3.0

Kolmogorov-Smirnov shows insignificant value less than 0.05

Variables are non-normally distributed

Location of median with respect to mean

Median < Mean Variables are skewed

Departure from symmetry is implied if the SE for skewness and kutrosis (if doubled) > value for skewness and kurtosis. For data from Kuala Kangsar, SE for skewness = 0.113 SE for kurtosis = 0.225.

Double SE for skewness is: 0.113 x 2 = 0.226; Double SE for Kurtosis is: 0.225 x 2 = 0.450 All skewness and kurtosis record values more than 0.226 and 0.450, respectively

Departure from symmetry is implied, thus variables are non-normally distributed

When transformations including natural logarithm, square root and inverse function are applied onto the variables for both datasets, none is able to normalize majority of the variables even when missing data are replaced and/or outliers are removed using the recommendation ��"'9:��7��9�"' [13, 14]. Departure from normality can also be checked by

finding SE

skewnessscorez =− and comparing it to 1.96 the

equivalent z-score for 05.0=α , which is also the boundary

value for assessment of normality [13], however this test is only practical on some of these variables.

Visualization using normal Q-Q plots and detrended normal Q-Q plots can also be used to confirm findings from the other tests. On both plots, each observed value is paired up with its expected value from the normal distribution. A variable that is normal will be demonstrated by values in a straight line for the normal Q-Q plot and values horizontally aligned along the line through 0 on the detrended Q-Q plots [15], as shown in Fig. 4 and Fig. 5 for the time duration between registration date and Form B.

Figure 4. Normal Q-Q plot - Time duration between

Registration Date and Form B

Figure 5. Detrended Q-Q plot – Time duration between

Registration Date and Form B

None of the data values are aligned on any of the straight lines in both graphs, thus these variables are non-normally distributed. Similar visualizations done for the other variables also report non-normality. Non-normal distributions with high skewness and kurtosis values can be heavy-tailed or light-tailed. Reference [16] states that a heavy-tailed plot will start from below the line, crosses the line then stays above the line while a plot that is symmetric will cross in the middle, thus the normal plots of the original data in this study exhibits the features of a heavy-tailed distribution.


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D. Justification for median absolute deviation as the best estimator for activity durations

A path in a NF model is any route from start to finish that can be critical or non-critical. The critical path measures the longest length through the network that determines the project duration, thus the major control on a NF model lies in successfully determining the critical path to avoid any activity delay that will ultimately impede the entire project. Hence, the study needs to include the process of selecting the best estimator for activity durations of the NF model as one of the criteria for the construction of the model. In particular, this section will attempt to justify the selection of median absolute deviation as the best estimator for activity durations.

Earlier conclusions indicate that variables involved are non-normal distributions that are heavy-tailed, thus there is need to include resistance to extreme values as a criterion for selection of the best estimator in order to determine a time window that will measure the efficiency of the estimator for activity durations. Mean is not resistant to extreme values, thus median is better to use in defining the measure of variation that will illustrate the degree of spread in the data activity. The size of the measure of variation determines how spread out the data activity is; large values will indicate that data are widely spread out while a small value means that the data is clustered around a certain value.

This section will attempt to establish that standard deviation (SD) has many drawbacks as a measure of variation for the said purpose of the current study. Where heavy tailed distributions are concerned, median absolute deviation (MAD), mean absolute deviation (AVAD) and inter-quartile range are better estimates of variation than SD [16]. Table 5 compares between five measures of variation, namely range, inter-quartile range, variance, SD and AVAD, with references to MAD in some places [14, 17].

Real data are never error free, and high quality data with typical errors may produce a slightly longer-tailed distribution than the normal distribution. Hence, amid the universal application of SD, Table 5 has shown that AVAD outperforms SD as a measure of variation in the presence of a hint of error in the distribution [17]. However, AVAD is more susceptible to extreme data in the tails than MAD. Therefore, MAD outperforms the other common measures of variation as the best choice of measure of variation to estimate activity times. The following subsections will proceed to define MAD then will attempt to establish MAD as an alternative to all other measures of variation in this study.

1) Definition of MAD

MAD defines the median of absolute deviations of data from the data median, thus, it is calculated using the formula #;��<=��=>< where <=>< is the median of the distribution. For example, consider the data set (1, 1, 3, 3, 5, 6, 7). Here, <=><�- and the absolute deviations about 3 will form the dataset (2, 2, 0, 0, 2, 3, 4) with ��#;��"

TABLE 5. COMPARING FIVE COMMON MEASURES OF VARIATION

Definition of Statistic Advantages Disadvantages ?�� ? �� $ �� @ ? � ABCDEFGH I ABJKFGH

Considers all values between two endpoints, Xlargest and Xlowest

Susceptible to extreme values. Does not take into account how data are actually distributed between Xlargest and Xlowest. Improper to use when there is at least one extreme value. L�� I M��$� �� LN? �� $��'.O��@ LN? � NP I NP

Considers all values between two endpoints, N2�Q��M��$� � ��NP��M��$� " Not influenced by extreme values.

Does not consider all values. Does not take into account how data are actually distributed between N2 �� NP.

Variance measures the average of the sum of the squared differences between the data and mean; R��$��&��7�4 S3� T ��U I �V WUX2� I �

Takes into account how the data are actually distributed. Evaluates how data fluctuates about the mean. Determines the number of data that falls within a specified interval in a distribution.

The computation results are in squared units.

Standard Deviation (SD) measures the square root of the average of the differences between the data and the mean; R��$��R��;�&��4 S� YT ��U I �V WUX2� I �

Takes into account how the data are actually distributed. Evaluates how data clusters around the mean. Provides the proportion of data that falls within 1SD, 2 SDs, or 3 SDs of the mean in a distribution. SD value is assured to be in the original unit of the data.

Due to squaring in the calculation of SD, SD is not able to provide a clear picture of the amount of variation that exists between the data and the mean as would AVAD. Provides misleading answers in cases with extreme scores. Advantage of SD does not exist for most social studies.

Mean Absolute Deviation (AVAD) specifies the average amount by which data deviates from the mean;

#Z#; � T [�U I �V[WUX2 �

Formula is easily understood. Can better measure the mean error of a series of observations than SD. Outperforms SD as an efficient statistic when there are small errors in the distribution and this efficiency is doubled if 5% of small errors are present in the distribution. Is better for use with distributions other than the normal distribution. AVAD works better with empirical data than SD.

The absolute value sign renders AVAD less useful as a measure of variation. AVAD is more affected by extreme data in the tails than MAD.

2) MAD as an Alternative to all Other Measures of Variation

Earlier discussions have indicated the superiority of AVAD over SD as a measure of variation. In addition, SD fails to be a reliable estimate in the presence of outliers, thus there is a need to use robust statistics to find the best estimator for activity durations. Robust statistics include methods that are largely unaffected by extreme values; among most commonly used statistics are median and MAD.

The level of robustness is measured using the global robust measure of reliability, the breakdown point (BP). BP determines the fraction of tolerable gross errors in a distribution before any statistic becomes unreliable; the higher the BP, the more robust the estimator. When more than 50% of the distribution is contaminated, it would not be possible to differentiate between the underlying distribution and the contaminated distribution, thus BP cannot exceed�� \ . On the other hand, if ]^�., the presence of a single outlier can cause the estimator to break down.


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MAD has a ]^�� \ , SD, AVAD and range have ]^�., and the inter-quartile range has ]^�� ,\ , thus MAD is more robust [18]. The discussions thus far have managed to show that MAD outperforms the range, the inter-quartile range, variance, standard deviation and AVAD as a robust statistic of the measure of variation, hence MAD is a measure of variation that can best estimate the activity durations in the proposed NF model. In particular, since median and MAD are both resistant to extreme values, both these measures will also define the time window for efficiency and effectiveness of the estimator for activity durations.

III. RESULTS AND DISCUSSIONS

Constitutional amendments are needed but they are not practical solutions to the predicaments faced by the Muslims. This prompted the current study to look into the possibility of finding an alternative practical solution from other areas than the legal system, that will lessen the degree of uncertainties and confusion among Muslims as well as to optimize time and money spent on processes to claim inheritance. The study has proposed the construction of a NF model that will provide clear guidelines for all activities in the claim process of Islamic inheritance. This proposed model has the advantage of being able to depict the activities according to their schedules whether concurrent or in series.

The success of the NF model will depend on its’ ability to estimate activity durations in the best possible manner that will enable the identification of shortest routes through the network. Hence, the statistic chosen for the purpose plays a fundamental role in the design of the network. The care and subtleties given in deciding that majority of the variables used are heavy-tailed and not normal provide the basis for using robust statistic to examine the superiority of MAD over the other measures of variation. Acceptable thresholds to decide departures from normality have also been used to confirm the non-normality result.

IV. CONCLUSIONS

There is currently no one single Syariah-compliant system for Islamic inheritance. In order to optimize time and money in the claim processes of Islamic inheritance, there is a necessity to search for a better solution elsewhere than the legal system. The proposed NF model should be able to divide the claim processes into significant activities using nodes and arrows, thus needs an estimator than can best estimate the activity durations to enable critical path analysis. Non-normality characteristics of data set form the basis for the selection of the best estimator for activity durations and also the time-window to measure efficiency and effectiveness of this estimator. In particular, the study has proven beyond doubt that MAD would be the measure of variation to best estimate the activity times for the NF model and to provide a time-window for measuring efficiency of the activity duration estimator. Future works in this area will look into the best method to optimize

time and money for the Muslims in petitioning claims to inheritance.

ACKNOWLEDGMENT The authors wish to thank Universiti Teknologi MARA for

supporting this study and the experts in the field of Islamic inheritance distribution at the Land Offices for sharing their experiences and expertise.

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[IEEE 2012 IEEE Symposium on Humanities, Science and Engineering Research (SHUSER) - Kuala Lumpur (2012.06.24-2012.06.27)] 2012 IEEE Symposium on Humanities, Science and Engineering