=Paper=
{{Paper
|id=Vol-3171/paper61
|storemode=property
|title=Sustainable Development by a Statistical Analysis of Country Rankings by the Population Happiness Level
|pdfUrl=https://ceur-ws.org/Vol-3171/paper61.pdf
|volume=Vol-3171
|authors=Myroslava Bublyk,Victoria Feshchyn,Lennara Bekirova,Olena Khomuliak
|dblpUrl=https://dblp.org/rec/conf/colins/BublykFBK22
}}
==Sustainable Development by a Statistical Analysis of Country Rankings by the Population Happiness Level==
https://ceur-ws.org/Vol-3171/paper61.pdf
Sustainable Development by a Statistical Analysis of Country
Rankings by the Population Happiness Level
Myroslava Bublyk, Victoria Feshchyn, Lennara Bekirova and Olena Khomuliak
Lviv Polytechnic National University, S. Bandera Street, 12, Lviv, 79013, Ukraine
Abstract
A statistical analysis of world rankings for the population happiness level was conducted to
find ways to stimulate sustainable development. The research is based on data from an annual
Gallup World survey called the World Happiness Report. Various data describing the
population's happiness level through direct (GDP per Capita, Social support, Life expectancy)
and indirect well-being indicators have been studied. The visualization methods, graphical
mapping in Cartesian and polar coordinate systems and primary statistical processing of
numerical data were used. We have used descriptive statistics, histograms, and cumulative
constructions. Linear smoothing was performed, and the GDP per Capita rating trend was used
to establish. Since the level of economic development and well-being of the population does
not correspond to its happiness, it is recommended to include the implementation of the
population's socio-historical, cultural and psychological traditions.
Keywords 1
Statistical analysis, information technologies, business analysis, sustainable development,
country rankings, Russian-Ukrainian war, level of population happiness
1. Introduction
The search for ways for sustainable development becomes relevant with each round of the new wars
threats on the planet. The level of happiness of the population is part of the annual Gallup World study
called World Happiness Report. Various data describe population happiness through direct (GDP per
capita, social support, life expectancy) and indirect welfare indicators. According to the authors' work
[1], the happiness rank of the world's countries is called to help government leaders, politicians, and
public figures better understand the needs and aspirations of their citizens to improve their well-being
and development. This ranking of happy countries considers the cost to the country of economic growth,
which is currently taking place in the social sphere, health, environment, and, ultimately, whether this
activity brings joy to the individual inhabitant of the kingdom.
The history of country rankings by the population happiness level began in 2006. The British
Research Foundation for Economics began calculating the International Happiness Index [2].
Interestingly, GDP figures were not considered in principle in 2006; as they say, in the end, happiness
is not in money. Authors [2] looked at three indicators: people's subjective satisfaction with life, life
expectancy, and "environmental footprint" - how people affect the environment. The main goal is to
show how effectively people in different countries use natural resources for a long and happy life. A
total of 156 countries were included in the ranking, and recently the leaders have only changed places,
but the essence has remained the same.
The authors of the study [3-4] believe that economic indicators maximally characterize human
capital development. Well-known economic indicators include many indicators [5-13]: GDP per capita,
COLINS-2022: 6th International Conference on Computational Linguistics and Intelligent Systems, May 12–13, 2022, Gliwice, Poland
EMAIL: my.bublyk@gmail.com (M. Bublyk); viktoriia.feshchyn.sa.2019@lpnu.ua (V. Feshchyn); lennara.bekirova.sa.2019@lpnu.ua
(L. Bekirova); olena.khomuliak.sa.2019@lpnu.ua (O. Khomuliak)
ORCID: 0000-0003-2403-0784 (M. Bublyk); 0000-0002-0291-643X (V. Feshchyn); 0000-0001-6991-9937 (L. Bekirova); 0000-0001-5249-
7889 (O. Khomuliak)
©️ 2022 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
social support, life expectancy, freedom of life choices, generosity (charity), trust (corruption) etc. The
modern economy is trying to explain what factors affect the happiness and well-being of the population
[14-25]. No less critical question for economists: when money ceases to matter to people, when the
majority of the population receives enough, what else, instead of GDP, what other factors need to be
assessed to understand - is the economy developing successfully?
The main goal of this work is to develop a concept of compiling a ranking of the happiest countries
based on relevant statistics. The purpose is the following. In this paper, we will try to get a little closer
to exploring the data collected in the World Happiness Report and find answers to questions about the
factors of the happy development of nations and the secrets of life in the happiest countries. To solve
this problem, we need to solve the following subtasks:
• Evaluate the available methods of solving the problem;
• Analyze the advantages and disadvantages of existing solutions;
• Justify the key components of the ranking of countries by the level of happiness of the
population.
The solution to the set tasks will have a practical application to stimulate sustainable development.
Statistical analysis of world rankings of happiness of the population will be useful to world leaders,
modern politicians and prominent public figures, substantiate the key needs of the population as a whole
in the country and the desire of each individual to improve their well-being. The received directions of
the needs for the happiness of the population of each country will allow to reconsider ways of
sustainable development and form the corresponding governmental decisions.
2. Related works
Ideas, implementation, and sustainable development indicators are set out in the 2030 Agenda for
Sustainable Development [26-28]. Priorities for sustainable development in the new Agenda included
the digitalization and ecologization of society and the development of smart cities [19, 20, 29-41].
Today, the search for sustainable development is at the crossroads between the long-lasting
consequences of the Covid-19 pandemic and the new round of full-scale Russian-Ukrainian war in
Ukraine. The World Happiness Report may seem inappropriate when children die in Ukraine. The
population of Ukraine suffers from the inhuman abuse of the Russian occupiers. According to [42], the
World Happiness Report 2022 paves the way for a new future with key knowledge for consumer brands.
According to [42], these data point to gaps in our development policies and people's perceptions of their
governments' work. The report [43] helps to point out the importance of qualitative development, not
quantitative. It considers what people think about women's rights, minority rights, corruption,
infrastructure development, education policy, fundamental rights, etc. The use of welfare has always
been essential to monitor the quality of life around the globe. In works [44-46], authors considered the
main task for most countries was to analyze the well-being of people and use these results to track and
explain the quality of life around the world. The primary source of quality of happiness among the
population was the organization Gallup, which conducts an annual World Survey. Still, this year the
authors decided to use more data to track satisfaction with the COVID-19 pandemic [45]. It is worth
noting that it was equally important to study how the geography of the virus and its consequences affect
public confidence, social and political status and how the rating is formed due to these factors. The
authors [46] also explained the differences between pre-pandemic and viral morbidity rates.
In [1, 4 – 6, 42], especially in the authors of the report Sustainability makes people happy, research
finds The World Happiness Report [25] believes sustainable development makes people happier.
According to a new study from the University of Oxford, progress towards the UN Sustainable
Development Goals includes goals such as adaptation to climate change and poverty eradication [26-
41]. According to a study published in Nature Scientific Reports [10], countries with a higher Center
for Sustainable Development index have better results in terms of subjective well-being, and Nordic
countries have both rankings. As countries become richer, the well-being of their citizens will remain
unchanged if further economic growth is not more sustainable, for example, by overcoming inequality,
according to [10].
The study also finds that while long-term environmental measures positively impact welfare, some
short-term sustainable development efforts may negatively correlate. This connection is partly due to
economic development, as countries with higher GDP tend to consume more due to higher living
standards. However, researchers found that low per capita consumption made people less happy even
when considering economical development. Researchers have identified several countries that maintain
prosperity and work well on sustainable consumption and emission reductions. The World Happiness
Report 2021 Media Round-Up on World Happiness and World Happiness Report 2022 was published
on March 20, 2021, covering more than 100 news stories worldwide [1]. The 2022 Report [6] shows
that Finland has taken the top spot as the happiest country. War-torn Afghanistan, Lebanon, Zimbabwe,
Rwanda, and Botswana are at the bottom of the list. The Russo-Ukrainian war escalated in February
2022 after the World Happiness Report data had already been collected. Today Ukraine is in the 98th
place in terms of happiness.
3. Methods
To solve the problems, we will use the following methods [47-54]:
• Construction of a mathematical model for data processing - the formation of a file with
numerical data in Excel format (text representation)
• Data visualization - a graphical representation with explanatory captions under and in the
figures
• Generalization of the data set - calculation of the most common statistical indicators, such as
mode, median, scope, arithmetic mean, and others
• Construction of the histogram (as the sample size is sufficient)
• The use of re-smoothing and straightforward methods with Kendall formulas.
4. Experiments and results
In researching the country rankings by the population happiness level, we considered the data [55],
which was created to help government leaders, politicians, and public figures better understand the
needs and aspirations of their citizens to improve their well-being and development (Fig.1).
4
3,5
3
2,5
2
1,5
1
0,5
0
Madagascar
Nigeria
Sri Lanka
Bangladesh
Colombia
Botswana
Canada
Saudi Arabia
Burkina Faso
China
Mexico
Italy
Kuwait
Central African Republic
Nepal
Panama
Czech Republic
Ireland
Ivory Coast
Yemen
Pakistan
Kazakhstan
Trinidad and Tobago
Tanzania
Venezuela
Congo (Kinshasa)
Paraguay
Kosovo
Lithuania
Taiwan
Swaziland
Turkmenistan
Family Health (Life Expectancy)
Freedom Trust (Government Corruption)
Generosity Dystopia Residual
Figure 1: Graphic representation of Happy Planet Index data
The Happy Planet Index (HPI) [55] consists of the following attributes: Country, Region, Happiness
Rank, Happiness Score, Standard Error, Economy (GDP per Capita), Family, Health (Life Expectancy),
Freedom, Trust (Government Corruption), Generosity, Dystopia Residual (Fig.1).
There are two coordinate systems of data representation called the Cartesian coordinate system and
the polar coordinate system chart. The economy (GDP per Capita) and Happiness Score are represented
in the Cartesian coordinate system (Fig.2, a), and GDP per Capita – in the polar coordinate system
(Fig.2, b).
1,8 8
1,6 7
1,4 6
Happiness Score
GDP per Capita
1,2
5
1
4
0,8
3
0,6
Economy (GDP per Capita)
0,4 2
Happiness Score
0,2 1
0 Costa Rica 0
Bangladesh
Israel
Mozambique
Zimbabwe
Zambia
Philippines
Saudi Arabia
Jamaica
Albania
Botswana
Latvia
Australia
Chad
Nicaragua
Uzbekistan
Jordan
Azerbaijan
Russia
Uganda
Gabon
Czech Republic
Japan
Luxembourg
Congo (Kinshasa)
Paraguay
Bahrain
a)
1
155157 3 5 7
151153 1,8 9
149 11
147 13
145 1,6 15
143 17
141 1,4 19
139 21
137 1,2 23
135 25
133 1 27
131 0,8 29
129 31
127 0,6 33
125 0,4 35
123 37
0,2
121 39
119 0 41
117 43
115 45
113 47
111 49
109 51
107 53
105 55
103 57
101 59
99 61
97 63
95 65
93 67
91 69
89 87 73 71
85 83 81 79 77 75
b)
Figure 2: Graphical representation of the Economy (GDP per Capita) and Happiness Score, where a) -
in the Cartesian coordinate system and b) - in the polar coordinate system
The Region means the region the country belongs to. Happiness Rank means the rank of the country
based on the Happiness Score. Happiness Score means a metric measured in period by asking the
sampled people the question: "How would you rate your happiness on a scale of 0 to 10&". Standard
Error means the standard error of the happiness score. Economic (GDP per Capita) means the extent to
which GDP contributes to calculating the Happiness Score. Family means the extent to which Family
contributes to calculating the Happiness Score. Health (Life Expectancy) means the extent to which
Life expectancy contributes to calculating the Happiness Score. Freedom means the extent to which
Freedom contributes to calculating the Happiness Score. Trust (Government Corruption) means how
Perception of Corruption contributes to Happiness Score.
Descriptive statistics are quantitative characteristics of data [56-70]. The task of descriptive statistics
in Excel is to use mathematical tools to reduce hundreds of sample values to several final indicators
that characterize the sample [47-54]. The following indicators are used: statistical mean, median, mode,
variance, standard deviation, etc. Descriptive statistics of country rankings by the population happiness
level are presented in Table 1.
Table 1
The Descriptive statistics of the GDP per Capita of the World Happiness Report
Index Value
Arithmetic mean 0,846137215
Standard error 0,032070567
Mode 0
Median 0,90198
Standard deviation 0,401843055
Sample Variance 0,162506362
Kurtosis -0,866986421
Skewness -0,317574652
Range 1,69042
Minimum 0
Maximum 1,69042
Sum 133,68968
Count 158
Confidence Level (95.0%) 0,063438752
The arithmetic mean (denoted by "Average") measures the major trend that reflects the most
characteristic value for a given sample. The formula determines it [47-54].
(1)
,
where n is the sample size.
The mode (denoted by "Mo") is a meaning found in this series more often than others and is often
used for non-parametric data and ranking scales [47-54].
The median (denoted by "Me ") of an ordered series of numbers with an odd number of members is
the number written in the middle, and the median of an ordered series of numbers with an even number
of members is called the mean arithmetic of two numbers written in the middle. It is a median equation
[47-54].
𝑛+1 (2)
𝑀𝑒(𝑛) = .
2
The range of numbers (interval) is an indicator that indicates the width of the range of values. It is
the difference between the largest and smallest of these numbers. For a more accurate idea of the values
variation of the indicator relative to the average, the coefficient of variation is used [71-81].
(3)
,
Coefficient of Variation (CV) is a relative measure of risk instead of variance and standard deviation.
It allows you to compare the risk and return of two or more assets that differ significantly [82-96]. In
data analysis, the coefficient of variation is used to compare the scattering of two random variables with
different units of measurement relative to the expected value, which allows for obtaining comparable
results.
Asymmetry is an indicator that reflects the skew of the distribution relative to the fashion to the left
or right. It is the case when any of the reasons contribute to the more frequent occurrence of values that
are greater or, conversely, less than the arithmetic mean [71-99]. Lower values are more common for
left-handed or positive asymmetry in the distribution than right-handed or negative. Excess is an
indicator that reflects the height of the distribution. When any reasons promote the emergence of close
to average values, the distribution with positive excess is formed. Suppose extreme values dominate the
distribution and, at the same time, lower and higher. In that case, such a distribution is characterized by
harmful excess, and in the centre of the distribution may form a depression, which turns it into two
vertices. The descriptive statistics analysis tool creates a one-dimensional statistical report containing
information about the initial range data's central trend and variability.
The boundary value intervals are indicated, and rectangles are constructed on their basis, the height
of which is proportional to the frequencies. The GDP per Capita by country rankings for the population
happiness level is shown in Fig.3.
1,8
1,6
1,4
1,2
1
0,8
0,6
0,4
0,2
0
31
43
13
19
25
37
49
55
61
67
73
79
85
91
97
1
7
103
109
115
121
127
133
139
145
151
157
Figure 3: Graphical representation of the economy (GDP per Capita) by country rankings by the
population happiness level
The distribution of the feature in the variation series on the accumulated frequencies is represented
by the cumulative. The cumulative is built on accumulated frequencies or frequencies. The value of the
sign is placed on the abscissa axis. The frequency accumulation is placed on the ordinate axis. In Fig.4,
the accumulated frequencies of the economy index are represented by the cumulative. 2. Identifying the
trend of the time series by smoothing methods
5. Discussion
5.1. Methods of smoothing time series
A time series is a set of measurements of a variable made over time. A characteristic feature of time
series is that observations of an object are carried out sequentially over time.
Cumulative
3
y = 0,0075x + 1,389
R² = 1
2,5
2
1,5
1
0,5
0
Lithuania
Romania
Malaysia
Swaziland
Liberia
Malawi
Israel
Brazil
Turkey
Nepal
Syria
Finland
United Kingdom
Bolivia
Mauritius
Ukraine
Djibouti
Uganda
Tanzania
Germany
Czech Republic
Tajikistan
Switzerland
Spain
Yemen
Ivory Coast
Japan
North Cyprus
Pakistan
Somaliland region
Trinidad and Tobago
Bosnia and Herzegovina
Figure 4: Cumulative of the economy (GDP per Capita) for the different countries ranked by the
population happiness level
For the analysis of the time series, the order in the sequence is essential, i.e., time is one of the
determining factors. Smoothing methods can be divided into two classes based on analytical and
algorithmic approaches.
The analytical approach is based on the assumption that the researcher can set a general view of the
function based on visual analysis, believing that its graph corresponds to the nature of the trend.
In other words, the analytical approach replaces the values of time series levels with values
theoretically calculated based on the explicit analytical form of the function, which approximates the
visually defined trend.
In the algorithmic approach, the appearance of the trend is obtained due to various algorithms that
practically implement smoothing procedures. These procedures provide the researcher only with an
algorithm for calculating the new value of the time series at any given time t.
The algorithmic approach classifies the following methods: - simple or ordinary moving average;
weighted moving average; exponential smoothing; median smoothing.
5.2. Moving average method
The average value of the levels included in the smoothing interval is in problems with a simple
moving average. Even when using large smoothing intervals, the effect, in this case, is not very
significant. Therefore, re-smoothing is used, increasing the window size for each re-approach. In this
case, the effect is significant.
The following table 2 with Kendall formulas implement simple moving averages because, for the
smoothing interval in the middle of the time series, which corresponds to the middle column of the
table, all weights are 1.
Table 2
The Kendell's formula, or simple smoothing (as example)
Turning
point w=3 w=5 w=7 w=9 w=11 w=13 w=15
FALSE
TRUE 1,3414366
FALSE 1,3622666 1,3619
TRUE 1,3702566 1,3406 1,3470414
FALSE 1,3585133 1,3460 1,3377842 1,3345755
TRUE 1,3153266 1,3473 1,3303357 1,3275833 1,3248481
TRUE 1,3171333 1,3055 1,3314928 1,3193888 1,2847818 1,2974107
TRUE 1,3037766 1,3070 1,2985742 1,2783111 1,2879554 1,26849 1,285426
FALSE 1,3051566 1,2946 1,2456442 1,2647811 1,2602336 1,2755815 1,2577413
TRUE 1,2707766 1,2199 1,2523557 1,2308088 1,2543709 1,2491015 1,2751806
TRUE 1,1726433 1,2210 1,2082271 1,2423933 1,2230027 1,2571715 1,2758793
FALSE 1,1738660 1,1751 1,2171985 1,2037044 1,2478809 1,2579153 1,2658006
TRUE 1,1045160 1,1873 1,1787785 1,2295044 1,2484736 1,2592669 1,2725326
TRUE 1,2507660 1,1378 1,2116828 1,2390355 1,2463018 1,2667923 1,2709406
TRUE 1,1320960 1,2594 1,2270242 1,2361733 1,2624009 1,2617661 1,2729853
FALSE 1,3132260 1,2592 1,2773157 1,2582511 1,2562909 1,2702223 1,2538206
5.3. Weighted moving average method
The method allows you to describe the primary trend of the series more accurately. When calculating
the weighted average of each level of the series within the smoothing interval, it is assigned a certain
weight, depending on the distance to the middle of the interval. It differs from the simple sliding method.
The levels included in the averaging interval of the weighted average variable and the simple moving
average are summed with different weights. A simple moving average considers all levels of the series
included in the smoothing interval with equal weights. The weighted average assigns to each level a
weight that depends on the distance to the interval middle.
The scales are symmetrical about the mid-level, and their coefficients are determined using the least-
squares method (LSM). There is no need to recalculate each time for the series levels included in the
smoothing interval, as they will be the same for each position. Also, the weights are always symmetrical
about the mid-level, their sum in the smoothing interval is equal to one, and the positive and negative
values of the weights provide the smoothed curve with the ability to reproduce the different curves of
the trend curve.
The moving average is not a scalar but a random process. The size of the subset from which the
average value is calculated can be both constant and variable.
The moving average may have weights, for example, to increase the impact of newer data compared
to older ones. Smoothing the original series gives an idea of the general trend of the series - its trend
and a cyclical component.
The result of linear smoothing of the Economy at w = 3 for the different countries ranked by the
population happiness level is shown in Fig.5.
1,6
1,4
1,2
1
0,8
0,6
0,4
0,2
0
116
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
101
106
111
121
126
131
136
141
146
151
156
w=3
Figure 5: The result of linear smoothing of the Economy at w = 3 for the different countries ranked by
the population happiness level
Properties:
1. When using the method of moving averages, choosing the value of the smoothing interval should
be made based on substantive considerations and tied to the period of possibly existing oscillatory
processes. If the average moving procedure is used to smooth the time series in the absence of any
fluctuations, the value of the smoothing interval is often chosen equal to three, five, or seven. The larger
the averaging (smoothing) interval, the smoother the trend chart.
2. Neighboring members of a series of moving averages are strongly correlated, as their formation
involved the same members of the original series. It may lead to several moving averages containing
cyclic components missing in the original series. This phenomenon is called the Slutsky-Yul effect.
3. As a method of averaging, in addition to the above-mentioned conventional arithmetic mean can
be considered as weighted moving averages, i.e., when the value of the original series in the smoothing
interval is summed with specific weights. Such procedures are appropriate if the change in time series
over time is nonlinear.
The result of linear smoothing of the Economy at w = 5 for the different countries ranked by the
population happiness level is shown in Fig.6. In Fig.7, we can see the result of linear smoothing of the
Economy at w = 7.
1,6
1,4
1,2
1
0,8
0,6
0,4
0,2
0
86
136
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
91
96
101
106
111
116
121
126
131
141
146
151
156
w=5
Figure 6: The result of linear smoothing of the Economy at w = 5 for the different countries ranked by
the population happiness level
1,6
1,4
1,2
1
0,8
0,6
0,4
0,2
0
6
1
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
106
101
111
116
121
126
131
136
141
146
151
156
161
w=7
Figure 7: The result of linear smoothing of the Economy at w = 7 for the different countries ranked by
the population happiness level
In Fig.8, we can see the result of linear smoothing of the Economy at w = 9. In Fig.9, we can see the
result of linear smoothing of the Economy at w = 11.
1,6
1,4
1,2
1
0,8
0,6
0,4
0,2
0 81
101
121
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
86
91
96
106
111
116
126
131
136
141
146
151
156
161
w=9
Figure 8: The result of linear smoothing of the Economy at w = 9 for the different countries ranked by
the population happiness level
1,4
1,2
1
0,8
0,6
0,4
0,2
0
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
101
106
111
116
121
126
131
136
141
146
151
156
161
w=11
Figure 9: The result of linear smoothing of the Economy at w = 11 for the different countries ranked
by the population happiness level
In Fig.10, we can see the result of linear smoothing of the Economy at w = 13. In Fig.11, we can see
the result of linear smoothing of the Economy at w = 15.
1,4
1,2
1
0,8
0,6
0,4
0,2
0
31
51
71
91
1
6
11
16
21
26
36
41
46
56
61
66
76
81
86
96
101
106
111
116
121
126
131
136
141
146
151
156
161
w=13
Figure 10: The result of linear smoothing of the Economy at w = 13 for the different countries ranked
by the population happiness level
1,4
1,2
1
0,8
0,6
0,4
0,2
0
141
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
101
106
111
116
121
126
131
136
146
151
156
161
w=15
Figure 11: The result of linear smoothing of the Economy at w = 15 for the different countries ranked
by the population happiness level
The rationing of time sequences makes it possible to compare the indicators obtained for different
objects because, in such rationing, the structure of the series (proportionality between levels in the
series) remains unchanged. It makes it possible to compare the calculated indicators and models based
on such data. The most commonly used linear transformation is that the values of the levels of the time
series lead to the range of values [0,1], using the following formula [31, 47-53].
𝑢𝑖 − 𝑦𝑚𝑖𝑛 (4)
𝑦𝑖𝑛 = ,
𝑦𝑚𝑎𝑥 − 𝑦𝑚𝑖𝑛 𝑖
where yin is the normalized value, yi is the current level value, ymin and ymax are the smallest and largest
values of a given time series level.
The criterion of efficiency of smoothing of time series is following
1. Criteria for turning points. To assess the smoothing effect, we propose using the criterion of
turning points, the content of which is the standard calculation of levels whose values are greater or less
than two adjacent.
2. Correlation coefficient. To estimate the closeness of the relationship between the original, we
propose using the original series and the smoothed correlation coefficient. The formula for calculating
turning points [47-54] is following.
𝐼𝐹 ((𝐼3 > 𝐼2); (𝐼3 > 𝐼4); 𝑂𝑅 (𝐼𝐹(𝐼3 < 𝐼2); (𝐼3 < 𝐼4))), (5)
The formula (6) determines the weighted moving average [100-105].
(6)
,
where pi- the value of the price of i -periods; Wi - the value of the scales for the price of i -periods ago.
The weighted moving average is the arithmetic weighted fluctuations of prices over a time period.
As an analytical tool, it removes some of the shortcomings of conventional sliding but does not
eliminate them.
5.4. Re-smoothing with Kendall formulas
Re-smooth the data using the dimensions of the smoothing interval w = 3, 5, 7, 9, 11, 13, 15 are
presented in Fig. 12-Fig.18. The smoothed data for GDP are calculated using to Kendall formulas [100-
105] for the smoothing interval w = 3 (Fig. 12), w = 5 (Fig. 13), w = 7 (Fig. 14), w = 9 (Fig. 15), w =
11 (Fig.16), w = 13 (Fig. 17), w = 15 (Fig.18).
W=3
1,6
1,4
1,2
1
0,8
0,6
0,4
0,2
0
21
106
1
6
11
16
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
101
111
116
121
126
131
136
141
146
151
156
Figure 12: Repeated simple Kendall smoothing and smoothing result at w = 3 for the different
countries ranked by the population happiness level
W=5
1,6
1,4
1,2
1
0,8
0,6
0,4
0,2
0
111
126
141
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
101
106
116
121
131
136
146
151
156
Figure 13: Re-smooth the GDP data using the dimensions of the smoothing interval w = 5 for the
different countries ranked by the population happiness level
W=7
1,6
1,4
1,2
1
0,8
0,6
0,4
0,2
0
66
146
1
6
11
16
21
26
31
36
41
46
51
56
61
71
76
81
86
91
96
101
106
111
116
121
126
131
136
141
151
156
Figure 14: Repeated simple Kendall smoothing and smoothing result at w = 7 for GDP of the different
countries ranked by the population happiness level
W=9
1,4
1,2
1
0,8
0,6
0,4
0,2
0
56
121
1
6
11
16
21
26
31
36
41
46
51
61
66
71
76
81
86
91
96
101
106
111
116
126
131
136
141
146
151
156
Figure 15: Re-smooth the GDP data using the dimensions of the smoothing interval w = 9 for the
different countries ranked by the population happiness level
W = 11
1,4
1,2
1
0,8
0,6
0,4
0,2
0
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
101
106
111
116
121
126
131
136
141
146
151
156
Figure 16: Repeated simple Kendall smoothing and smoothing result at w = 3 for the different
countries ranked by the population happiness level
W = 13
1,4
1,2
1
0,8
0,6
0,4
0,2
0
61
1
6
11
16
21
26
31
36
41
46
51
56
66
71
76
81
86
91
96
101
106
111
116
121
126
131
136
141
146
151
156
Figure 17: Repeated simple Kendall smoothing and smoothing result at w = 3 for the different
countries ranked by the population happiness level
W = 15
1,4
1,2
1
0,8
0,6
0,4
0,2
0
66
81
96
111
126
1
6
11
16
21
26
31
36
41
46
51
56
61
71
76
86
91
101
106
116
121
131
136
141
146
151
156
Figure 18: Repeated simple Kendall smoothing and smoothing result at w = 3 for the different
countries ranked by the population happiness level
Thus, linear smoothing was carried out to establish the GDP per capita rating trend. Novelty is
following. Certain trends and patterns that affect the happiness and well-being of the population have
been identified. It is proposed to shift the attention of economists to the importance of qualitative
development rather than quantitative. As the level of economic development and well-being of the
population does not correspond to its happiness, it is recommended to include the introduction of socio-
historical, cultural and psychological traditions of the population in the world. It is proposed to use the
obtained results to improve sustainable development goals further and expand them with new value
blocks of social responsibility.
6. Conclusions
To find ways to stimulate sustainable development, we conducted a statistical analysis of world
rankings of the level of happiness of the population. Various data describing the population happiness
level through direct (GDP per capita, social support, life expectancy) and indirect welfare indicators
have been studied. Imaging methods, graphical display in Cartesian and polar coordinate systems and
primary statistical processing of numerical data are used. We used descriptive statistics, histograms and
cumulative constructions. Linear smoothing was carried out to establish the GDP per capita rating trend.
Novelty is following. Certain trends and patterns that affect the happiness and well-being of the
population have been identified. It is proposed to shift the attention of economists to the importance of
qualitative development rather than quantitative. As the level of economic development and well-being
of the population does not correspond to its happiness, it is recommended to include the introduction of
socio-historical, cultural and psychological traditions of the population in the world. It is proposed to
use the obtained results to improve sustainable development goals further and expand them with new
value blocks of social responsibility.
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