There are three main pear production regions in Hungary. The most relevant is theWest-Transdanubian (Zala, Vas and Gyôr-Moson-Sopron counties), where up to 30% of total pear production occurs. The second most productive region is Pest County, where pear is grownmostly in gardens and garden plots, resulting in 15-20% of Hungarian production. In the northern Hungarian region (Bodrog valley in Borsod-Abaúj-Zemplén, Heves and Nógrád counties), the microclimate is perfect for optimal pear production. In our analysis, we focused on fourplantations that are dominant in pear production in Hungary. Two of them are situated in south-western Hungary, one of them is in SouthTransdanubia and one is in North Hungary. Considering the personal attitude of the decision maker towards risk, the best alternative is ‘Williams’in Alsóberecki, as the yield risk is the lowest with this variety, while the second best alternative is ‘Bosc Beurre,’ also produced in Alsóberecki.This is an irrigated area, and this fact evidently decreases the yield risk. The highest risk is in Bánfapuszta and in Zalasárszeg, for the non-irrigated‘Williams’ variety. The highest yield with the lowest risk can be obtained with irrigation. Nevertheless, in the case that relevant data are available,and by incorporating cost and expected profit data, the stochastic dominance method is suitable for financial risk assessment, as well

I., Ertsey

J., Nyéki

M., Ladányi

M., Soltész

Sz., Persely

Z., Szabó

University of Debrecen Electronic Archive

Introduction
Hungary does not number among the greatest European
pear producing counties. The area of pear plantations is only
8-10% the size of the total area of the apple orchards. Earlier,
between 1981 and 1984, 100 thousand tonnes of pears were
harvested and during this boom, similarly to the European
pattern, varieties were cultivated which could handle higher
levels precipitation and humidity. Since 1985, production has
been decreasing. While in 1985, 10900 ha were used as pear
plantations, this figure was 13800 ha in 1994 and 3200 ha in
2007 (FAO). Plantations are mainly situated in southern
Hungary and West-Transdanubia. In West-Transdanubia,
almost one-half of the plantations exceed 25 ha, while they
are predominantly between 10 and 15 ha in the south (KSH).
The most important varieties are ‘Bosc Beurre’ (32%) and
‘Williams’ (18.5%), followed by ‘Conference’ and
‘Packhams’. In Europe, the yearly average consumption per
capita for pear is 5 kg and only 1.5 kg in Hungary. Hungarian
producers would like of course to reach levels of domestic
consumption more on a par with that in the rest of Europe.
For this wider range variety selection, improved production
and processing technology are necessary. Drimba and Nagy
(1997, 1998, 2000), as well as Drimba and Ertsey (2003)
pointed out that yield risk has an important role in
production. Our aim was to compare four different
plantations with different agro-ecological characteristics,
together with two different pear varieties (‘Bosc Beurre’ and
‘Williams’) from the aspect of yield risk and considering the
personal attitude of the decision-maker towards risk.
Material and methods
The examined fruit varieties
• ‘Bosc Beurre’
‘Bosc Beurre’ is the most widely cultivated variety in
Hungary. It is well-known worldwide, with its distinctive
characteristics being its brown skin, which holds a delicious,
sweet-spicy flavoured and slightly firmer flesh, which while
a bit crunchy, remains tender. It has a long, curved stem with
a neck that widens gradually into a round shape (Göndörné,
2000). Russetting may cover the entire surface of the pear
(Soltész, 1998). Harvest is usually in mid September. The
tree is medium sized or slightly weak. The size of the fruit is
large or extra large (180–280 g), showing little colour change
as it ripens.
• ‘Williams’
In Hungary, this is the second most important variety
after the ‘Bosc Beurre’. It has a classical "pear shape": a
rounded bell on the bottom half of the fruit, with a definitive
shoulder and a smaller neck or stem end (Göndörné, 2000,
Comparison of pear production areas from yield risk aspect
Persely, Sz.1, Ladányi, M.2, Nyéki, J.3, Szabó, Z.3, Soltész, M.3 & Ertsey, I.1
1University of Debrecen, Centre for Agricultural Sciences and Engineering, Department of Economic Analysis
and Statistics, H-4032 Debrecen, 138 Böszörményi, Hungary, E-mail: suto@agr.unideb.hu
2Corvinus University of Budapest, Department of Mathematics and Informatics, H-1118 Budapest, 29-43 Villányi,
Hungary, E-mail: marta.ladanyi@uni-corvinus.hu
3Institute for Research and Development, University of Debrecen, H-4032 Debrecen, 138 Böszörményi, Hungary,
E-mail: nyeki@agr.unideb.hu
Summary: There are three main pear production regions in Hungary. The most relevant is theWest-Transdanubian (Zala, Vas and Gyôr-Moson-
Sopron counties), where up to 30% of total pear production occurs. The second most productive region is Pest County, where pear is grown
mostly in gardens and garden plots, resulting in 15-20% of Hungarian production. In the northern Hungarian region (Bodrog valley in Borsod-
Abaúj-Zemplén, Heves and Nógrád counties), the microclimate is perfect for optimal pear production. In our analysis, we focused on four
plantations that are dominant in pear production in Hungary. Two of them are situated in south-western Hungary, one of them is in South
Transdanubia and one is in North Hungary. Considering the personal attitude of the decision maker towards risk, the best alternative is ‘Williams’
in Alsóberecki, as the yield risk is the lowest with this variety, while the second best alternative is ‘Bosc Beurre,’ also produced in Alsóberecki.
This is an irrigated area, and this fact evidently decreases the yield risk. The highest risk is in Bánfapuszta and in Zalasárszeg, for the non-irrigated
‘Williams’variety. The highest yield with the lowest risk can be obtained with irrigation. Nevertheless, in the case that relevant data are available,
and by incorporating cost and expected profit data, the stochastic dominance method is suitable for financial risk assessment, as well.
Key words: pear, yield, mean-variation efficiency, stochastic dominance
International Journal of Horticultural Science 2010, 16 (4): 25–28.
Agroinform Publishing House, Budapest, Printed in Hungary
ISSN 1585-0404
26
2001). This pear is extremely aromatic. The
size of the fruit is large or extra large
(160–220 g) (Soltész, 1998). It is harvested
from late August to early September. This
pear is unique, in that its skin colour
brightens as it ripens, unlike other varieties.
Its flavour is sweet delicious when it reaches
a golden yellow ripening stage. In addition to
eating it fresh for its smooth texture,
‘Williams’ is also traditionally known as a
canning pear variety.
The examined plantations
• Zalasárszeg
The Zalasárszeg plantation is situated in
south-western Hungary. There are 45 ha of
‘Bosc Beurre’ and 12 ha of ‘Williams’ orchards there. The
orchard in Zalasárszeg planting design is 9 x 5 m. Trees were
trained to spindle. Plantation is grassed and non-irrigated.
• Bánfapuszta
Bánfapuszta plantation is also situated in south-western
Hungary. ‘Williams’ and ‘Bosc Beurre’ were grown on 44.5
ha and 32.3 ha in 1994, respectively, while the areas of the
plantations are now 15.7 ha and 18.5 ha. Planting design of
Bánfapuszta is 6 x 4 m. Trees are spindle shaped without
support system and the plantation is grassed and non-
irrigated.
• Alsóberecki
Alsóberecki can be found in Borsod-Abaúj-Zemplén
County, 85 kilometres northeast of Miskolc, in the Bodrog
River valley. The plantations were planted in 1974 and 1975.
There are 25 ha of ‘Bosc Beurre’ and 8 ha of ‘Williams’
orchards there. The trees are trained to hedgerows with
slanting branches. Its crown shape is bushy, a wild type of
fruit tree, ‘Bosc Beurre’ was grafted on seedings, ‘Williams’
grafted on quince.
• Siófok
Siófok is situated in Transdanubia, on the south-eastern side
of Lake Balaton. The surface is slightly rolling with west-facing
slopes and no groundwater to a depth of 200 cm. Its ecological
characteristics are excellent, with almost no frost risk. The entire
area can be irrigated. The pear orchard is 5.5 ha and was first
planted in 1988. The main variety is ‘Williams’with ‘Clapp’ as
polliniser. Both varieties are grafted to quince, trained to spindle.
The method of the risk analysis
During our analysis, we used the mean-variance (E-V)
efficiency method, first and second degree stochastic dominance
(FSD, SSD), as well as those general stochastic dominance
methods which consider the intensity of risk aversion of decision
Persely, Sz., Ladányi, M., Nyéki, J., Szabó, Z., Soltész, M. & Ertsey, I.
Figure 1. The examined pear varieties (‘Bosc Beurre’ and ‘Williams’)
Figure 2. The examined plantations
27
makers. With the help of these methods, the
yield risks on four different plantations were
compared (Persely et al., 2010).
Results
We used the E-V efficiency criterion to
compare the yield risk of four different
plantations (Bánfapuszta, Zalasárszeg, Alsóbe-
recki and Siófok) and two pear varieties
(‘Williams’, ‘Bosc Beurre’) (Figure 3). The
efficient set contains the points of the
alternatives in the north-west quadrant, which is
empty. From among the examined variations,
the ‘Williams’ and ‘Bosc Beurre’ varieties
cultivated in Bánfapuszta, as well as the
‘Williams’cultivated in Siófok, do not belong to
the efficient set. Since fromamong the examined
alternatives only some of these may be placed in
any determinable order, we calculated the first
and second degree stochastic dominances.
In Figures 4 and 5, we can see the results
of the first and second degree stochastic
dominance. In Figure 4, the distribution
functions cross each other, so again only
partial dominance can be proved between the
alternatives with this method. We cannot
define the alternative(s) with the less yield
risk exactly; however, we can see that the
distribution functions of Alsóberecki
alternatives are located to the right of the
other distribution functions on almost the
whole domain. Moreover, the slopes of the
distribution functions above the 0.1
probability range seem to be higher than the
ones of the other functions, which indicates
higher expectations with lower variances and
therefore relatively lower risk.
In order to determine the ranking of
alternatives, one must employ the second
degree stochastic dominance method (Figure
5). It can be seen that ‘Williams’ has the
smallest yield risk in Alsóberecki, since the
integral of its distribution function lies
everywhere below and to the right of the other
curves. It is followed by the ‘Bosc Beurre’ in
Alsóberecki and by the ‘Bosc Beurre’ in
Bánfapuszta. However, with the help of the
second degree stochastic dominance we cannot
show total ordering as some curves still cross
each other. Nevertheless, the general stochastic
dominance method is applied not only for the total ordering but
also for considering the risk aversion of the decision maker.
If we represent the certainty equivalent (CE) curves with
the help of the general stochastic dominance method, we can
compare the four different plantations and the two pear
varieties according to their yield risk. The main advantage of
this method is that the decision makers’ personal attitude
towards risk can also be considered. The higher the CE curve
of the risk aversion lies the lowest risk the alternative
contains (Persely et al., 2010).
Comparison of pear production areas from yield risk aspect
Figure 3. E-V efficiency for four different plantations and two pear varieties (‘Williams’ and ‘Bosc
Beurre’)
Zala_Williams
Zala_Bosc Beurre
Alsó_Williams
Alsó_Bosc Beurre
Siófok_WilliamsBánfa_Williams
Bánfa_Bosc 
Beurre
0
5
10
15
20
25
30
35
0 20 40 60 80 100 120
E (kg/ha)
V
E-V efficiency
Figure 4. Illustration of first degree stochastic dominance. The distribution functions are for the
yield of four different plantations and to ‘Williams’ and ‘Bosc Beurre’ pear varieties
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
0 10 20 30 40
F
t/ha
First degree stochastic dominance
Alsóbereczki Williams
Alsóbereczki Bosc Beurre
Bánfa Bosc Beurre
Zala Bosc Beurre
Siófok_Williams
Bánfa_Williams
Zala Williams
Figure 5. Illustration of second degree stochastic dominance for the yield of the examined four
plantations and for the two pear varieties.
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
0 50 100 150 200 250 300 350 400
Second degree stochastic dominance
Alsóbereczki Williams
Alsóbereczki Bosc Beurre
Bánfa_Bosc Beurre
Zala Bosc Beurre
Siófok_Williams
Bánfa_Williams
Zala Williams
28
As can be seen in Figure 6, on the left, the CE curve of
variety ‘Williams’ from Alsóberecki lies the highest, so this
alternative has the lowest yield risk. This alternative is followed
by ‘Bosc Beurre’ from Alsóberecki, Bánfapuszta and
Zalasárszeg. The enlarged CE curves of variety ‘Williams’
from Siófok, Bánfapuszta and Zalasárszeg are displayed in
Figure 6, on the right. As can be seen on this figure, if the risk
aversion is low (ra < 0.008), the better alternative is ‘Williams’
from Bánfapuszta, while in case the risk aversion is higher (ra >
0.008), ‘Williams’ from Zalasárszeg is the better alternative for
the decision maker.
Acknowledgements
Herewith we would like to express our thanks to Miklós
Csengô, József Szukics, Gyula Sipos and Cecília Konrád-
Németh for their inspiration and assistance, and to the research
projects: OM-00042/2008, OM-00265/2008, OM-00270/2008
for supporting the research.
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Figure 6. Certainty equivalent curves for the yield risk of the examined four plantations and for the two varieties, depending on the risk aversion value (ra) of
the decision maker
5
7
9
11
13
15
17
19
21
23
25
27
29
31
0 0,002 0,004 0,006 0,008 0,01
CE (t/ha)
r_a
General stochastic dominance
Alsóbereczki Williams
Alsóbereczki Bosc Beurre
Bánfa_Bosc Beurre
Zala Bosc Beurre
Siófok_Williams
Bánfa_Williams
Zala Williams
11,7
11,8
11,9
12
12,1
12,2
12,3
0 0,002 0,004 0,006 0,008 0,01
CE (t/ha)
r_a
General stochastic dominance
Siófok_Williams
Bánfa_Williams
Zala_Williams


Comparison of pear production areas from yield risk aspect

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Comparison of pear production areas from yield risk aspect

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