Coconut statistics - Lin Yangchen
©Lin Yangchen

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Variations in stamp production are influenced by an interplay of geography, postal dynamics and even human psychology. But the patterns are hard to discern unless one is able to observe and track high-throughput stamp production over a considerable span of space and time.

For this kind of analysis, copious amounts of data are needed on a long-lived stamp series, and not only that. The series must have location-dependent design variants that allow one to study spatial patterns. Not many stamp series fulfill all these criteria. Even if they do, their data may not be available or accessible.

The post-war coconut definitives turn out to be ideal for the task. They were produced from 1947 to 1958, with different vignettes for different states. There were 19 values from 1¢ to $5, giving much additional latitude for studying abundance and usage patterns. Being definitives they were produced in large quantities, though not on the scale of the Penny Lilac.

This study is the first such analysis of Malayan material, and reveals emergent nonlinear patterns of large-scale stamp production that are also found in many other natural and man-made phenomena. The full article appears in The London Philatelist (Lin 2018e).


This study was made possible by the fact that Stanway (2009) painstakingly compiled comprehensive stamp requisition figures for the coconut definitives from primary sources. I used the data on the quantities of stamps ordered by the Crown Agents, broken down into individual orders, denominations and states. Since almost 200 orders were made frequently over the span of a decade instead of one large order, the quantities ordered should be reasonable indicators of actual demand, with a small time lag.

A small number of orders were omitted from the analysis. Some of these had been cancelled for various reasons and no stamps were printed. Two orders for Kedah and Perak had stamps printed, but the quantities were not recorded. These missing data should not affect the analysis qualitatively, since they were probably small orders for which documentation was not crucial.

The 12 states were characterised using various basic measures; see Table 1 in Lin (2018e). State areas are mostly data from the year 2000 in the Wikipedia article Demographics of Malaysia. For Singapore, which has undergone extensive land reclamation since independence in 1965, its total land area in 1960 was obtained from the Singapore government’s website

State populations in 1947 and 1957 were taken from Sultan Nazrin Shah (2016), Singapore’s National Library Board website, and Chua (1964). For each state, the mean of the 1947 and 1957 populations was calculated. This serves as a measure of the population coinciding with the middle of the stamps’ period of production, assuming the population increased steadily.

The approximate duration for which the coconut definitives were in circulation for each state was calculated based on earliest date of release for the state and the date of invalidation of the majority of denominations in the state. These data were obtained from Stanway (2009) and converted to Julian dates. The release date was then subtracted from the invalidation date to get the number of days.

Permutations and quantities

A permutation is defined in this study as a stamp of particular combination of state, head, denomination and colour, for example Penang, King George VI, 8 cents, green. This is distinct from varieties, which are stamps of the same “permutation” with different plate flaws, subtle variations in shade etc.

Two of the three rarest post-war non-BMA permutations of the coconut definitive.

I ranked the 281 permutations of the post-war coconut definitives by quantity produced. It is no surprise that top values from remote states were the rarest: Perlis $2 and $5 and Trengganu $5 (see full table of rankings). There were 57,000 printed of each of these three. These, however, are not the rarest permutations of the coconut definitive overall; the BMA $5 on green paper holds the record with fewer than 12,000 copies made. On the other extreme, about 86 million Singapore 10¢ were printed. I saw it myself; my grandfather had boxes and envelopes stuffed full of Singapore 10c stamps from daily business letters. My grandmother helped soak the stamps off. Elsewhere, many 10¢ stamps ended up on student savings cards. The difference in abundance between the commonest and rarest permutations of the coconut definitive is more than 1,500-fold.

A word of caution about Singapore: the change in perforation occurred during the first printing, and the respective quantities are unknown. It is also not known whether the gauge-14 perforator continued to be used or not after the manufacturers started using the smaller-gauge perforator. The Singapore data therefore does not distinguish the two perforation sizes, and the abundance ranking pools the two perforations for each denomination.

The ranked abundances of permutations follow a long-tailed distribution. A power-law fit yielded an exponent of 1.78. The Kolmogorov-Smirnov statistic was a relatively small 0.0638 with a large p-value of 0.54, indicating that the data fit a power law reasonably well. Power laws are characterised by scale-invariance; the shape looks the same no matter how much you zoom in. Examples abound in natural and manmade phenomena, from the size of craters on the moon to the frequency of words in languages.

Abundance ranks of permutations, by denomination. Each panel takes the ranking from Fig. 4 and shows the positions of the permutations of the respective denomination as vertical lines. The permutations within most denominations are quite variable in abundance, suggesting that differences between states are the main determinants of abundance. For the commonest and rarest denominations (10¢ and $5 for example), however, the postal purpose of the denomination probably outweighed differences between states, resulting in the permutations being less variable in abundance.

Relationship between the total number of stamps of a denomination, and the range in abundances of its permutations.

The range of abundances of the permutations of each denomination was calculated by taking the difference between the commonest and rarest permutation of each denomination. That was then plotted against the number of stamps. Numbers within the plot refer to denominations. A unimodal relationship seems evident: very rare or very common denominations are rare or common across all states, since their abundance is largely dependent on the denomination’s purpose and the corresponding demand for it. In contrast, denominations of intermediate rarity can be rare in some states and common in others depending on geographical and anthropological factors. This recalls the intermediate disturbance hypothesis in ecology: species diversity is highest when ecological disturbance is neither too rare nor too common.

The 1¢, 2¢ and to some extent 3¢ appear to be outliers with intermediate abundance but low abundance range. This could be because they are very low denominations for which it was not critical to match supply and demand very accurately to the needs of each state. It was probably easier to submit similar-sized orders for different denominations.

The large number of varieties was spawned by a combination of geographical segmentation, changes in postage rates and royal succession. For example, the 8¢ and 20¢ underwent colour changes in 1951 in compliance with Universal Postal Union standards. Several values were replaced by new values as postage rates changed (see Stanway 2009 for details). For example the 40¢ was replaced by the 35¢, and in turn by the 30¢ airmail rate in 1952 and 1955 respectively. The colour scheme of red and purple was used for all three. In addition, the portrait of King George VI on the stamps of Penang and Malacca had to be changed to Queen Elizabeth II in 1953.

The lowest denominations increase sequentially, followed by mostly even numbers, and in turn by higher values mostly in multiples of 5 since increasing by smaller amounts does not make much difference at larger scales. This contrasts with earlier stamps, say the Imperium classics where one sees sequences like 24¢–25¢ (British Honduras Queen Victoria) and 12¢–13¢ (Seychelles Queen Victoria), just to name a couple.

Modern stamp series tend to have considerably fewer denominations. This could be because postage rates have been simplified. Today, the post office might stipulate a single air mail rate no matter which route the mail takes, the same rate for all overseas mail, and fewer weight categories, et cetera.

Denominations and requisitions

Overall production of each denomination. The rarest denomination is the $5 while the most common denominations are 10¢ followed by 4¢, which come as no surprise to collectors familiar with the series.

As the denomination increases, the average requisition size for that denomination falls. The authorities may have followed subconscious sensibilities even as they tried to tailor quantities to specific circumstances. The high-output 4¢ and 10¢ have been omitted to show the main relationship more clearly. The logarithm of the denomination gives a linear relationship (least-squares-fitted line shown) because the sequence of denominations is perceived as equidistant discrete entities for purposes of requisition, but are in fact values of a continuous variable spaced further and further apart as denomination increases. This concept is illustrated by the fact that the difference between 1¢ and 2¢ is much smaller than the difference between $1 and $2, although both pairs are adjacent denominations.

Ranked barplot of requisition sizes, by denomination. The total area of bars for each denomination is proportional to the total number of stamps ordered. In denominations with a large number of orders, a long-tailed distribution emerges in the ranked order sizes. Stepped structures are often seen; this could be because the authorities, being humans, tended to pick certain numbers that looked nice to them.

The larger the number of requisitions, the larger the total number of stamps printed. A few extreme cases make the relationship nonlinear. The 10¢ and 4¢ were in such high demand that orders had to be disproportionately big.


Examination of the data shows that states differ little from one another in relative stamp quantities across denominations, simply following the overall trend. This indicates that there was little variation across states in postal habits such as local versus overseas mail.

The number of requisitions was quite similar across states. This indicates that requisitions were planned out, not haphazard, despite the fact that each state had separate orders. Johore had more orders because Sultan Ibrahim did not approve of a new definitive design and the coconut definitives had to be printed until he died in 1959. The small numbers of orders for Perlis and Malacca are no surprise as their populations are among the smallest.

Population density accounts for both population and area, and could be taken as an indicator of overall urbanisation and communications. There is a positive nonlinear relationship between a state’s population density and the number of stamps, even after the number of stamps has been adjusted per capita. This suggests that people living in more urbanized and crowded places correspond more frequently and with more people, which makes sense. They have the means and desire to travel more widely and meet more acquaintances. A big city also requires more administrative coordination and correspondence to run smoothly.

East coast states tend to have lower population density and fewer stamps than those on the west coast. The west is more developed as it fronts the Straits of Malacca, a major maritime highway that famously has Singapore at its crossroads. Indeed, the two square data points, corresponding to Johore and Singapore, show that they were a world apart despite being adjacent to each other and both having access to the west coast. Location and area are interacting factors here.

A geographical visualization of the number of stamps printed per capita per year reveals other things. Despite its trading vintage, Malacca had receded to a postal backwater compared with Singapore and Penang. And despite the enormous overall quantity of coconut definitives produced for Johore over a prolonged period, it falls behind the more industrious states and even jungle-clad Pahang in stamps available to each person per unit time. While the sprawling Malay states occupied themselves with the extraction of natural resources like tin, rubber and rice, petite Singapore focused on channeling goods into and out of the peninsula. This meant lots of correspondence and lots of stamps.

The fact that stamps from any Malayan state could be used in any other state is a possible confounding factor. This, however, is significant only if supply does not match demand and if there is frequent interstate travel. It is unlikely to qualitatively affect the findings, because post offices have to constantly issue the right stamps in the right places and would detect and act on any shortfalls or oversupply quite quickly.

Temporal dynamics

Overall production of the post-war coconut definitives by year. The time dimension reveals additional insights not otherwise apparent. The initial burst of production was followed by a bigger burst of resupply in the middle. Requisitions then tailed off with later orders put in just to top up supplies before the next definitive issue was inaugurated.

Stamp production by year, for each denomination. Solid lines are to the same scale across panels, while the dotted lines have been expanded to fill the y-axis for each denomination, to make it easier to see the temporal fluctuations.

The workhorse values like 4¢, 10¢ and 25¢ set the overall trend. Meanwhile a few values, particularly the 8¢, 20¢ and $5, show oscillations that are large relative to their quantities. I speculate that this might have been due to time lags in responding to demand, which in turn was made challenging by the difficulty of gauging demand for low-production denominations. The colour changes of the 8¢ and 20¢ were contributing factors too, coinciding with the first big spike. Demand for the 1¢ and 2¢ does not appear to have been very high. These denominations served mainly to make up required postage rates (e.g. Chua 1989). Meanwhile requisitions dropped to zero for those denominations that were replaced by new values (see earlier part of article).


This study shows the potential use of large and comprehensive datasets in gaining a deeper understanding of the socioeconomic, geographical and even psychological forces that influence the ups and downs of postage stamps.

Further research could explore other long-lived, widespread stamp series to discover how universal the patterns are. Hopefully this will widen the relevance of philately in offering insights for other disciplines.


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